Daily Papers

The cosmology of the F(R) gravity rebuilding by the Cartan formalism is investigated. This is called Cartan F(R) gravity. The well-known F(R) gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan F(R) gravity is based on the Riemann-Cartan geometry. The curvature R can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan F(R) gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of \(2\to2\) scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons \((TTT)\) and Abelian gauge currents \((TJJ)\), through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated \(4\)-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

We provide a well-defined variational principle for 3-dimensional flat space Einstein gravity by adding one half of the Gibbons-Hawking-York boundary term to the bulk action. We check the 0-point function, recovering consistency with thermodynamics of flat space cosmologies. We then apply our result to calculate the 1-point functions in flat space Einstein gravity for the vacuum and all flat space cosmologies. The results are compatible with the ones for the zero mode charges obtained by canonical analysis.

Core collapse supernovae are among the most energetic astrophysical events in the Universe. Despite huge efforts on understanding the main ingredients triggering such explosions, we still lack of compelling evidences for the precise mechanism driving those phenomena. They are expected to produce gravitational waves due to asymmetric mass motions in the collapsing core, and emit in the meanwhile neutrinos as a result of the interactions in their high-density environment. The combination of these two cosmic messengers can provide a unique probe to study the inner engine of these processes and unveil the explosion mechanism. Among the possible detectable signature, standing accretion shock instabilities (SASI) are particularly relevant in this context as they establish a direct connection between gravitational wave emission and the outcoming neutrino flux. In this work, Hilbert-Huang transform is applied to a selected sample of 3D numerical simulations, with the aim of identifying SASI contribution and extract its instantaneous frequency. The performance of the method is evaluated in the context of Einstein Telescope.

We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L_{infty} algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L_{infty} algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L_{infty} algebra on the boundary. The resulting action is the `on-shell action' conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L_{infty} algebras.

We demonstrate how horizon symmetries of AdS black holes are realised in the hydrodynamic actions for the dynamics of the dual stress tensor. A recent approach for obtaining such actions involves a choice of horizon boundary conditions, and we show that diffeomorphisms that preserve these give rise to symmetries of the corresponding hydrodynamic action. We obtain explicit hydrodynamic actions for small amplitude perturbations of black holes in JT and AdS_3 gravity using this approach and demonstrate explicitly the existence of these symmetries. For a natural choice of boundary conditions, the resulting actions manifestly realise gauge symmetries previously proposed for effective theories of maximal chaos.

Let X be an algebraic variety over C and G be an algebraic group acting on X whose action is closed. J. Poineau defined a compactification X^urcorner of X(C) by using hybrid Berkovich spaces. We will focus on the extension of the action of G on this compactification by characterising the set U subset X^urcorner where the action is well defined. We will also show that the quotient of U by the action of G is homeomorphic to (X/G)^urcorner, the compactification of (X/G)(C). We then apply these results to X = Rat_d, the space of rational maps and G = SL_2. It gives the results of C. Favre-C. Gong in a more general setting. Furthermore, we get a compactification of M_d = Rat_d/SL_2 where the boundary is made of orbits of non-archimedean rational maps. The results still holds if C is replaced by k a non-trivially valued field and complex analytic spaces by Berkovich spaces over k.

Riemannian four-manifolds in which the triple contraction of the curvature tensor against itself yields a functional multiple of the metric are called weakly Einstein. We focus on weakly Einstein K\"ahler surfaces. We provide several conditions characterizing those K\"ahler surfaces which are weakly Einstein, classify weakly Einstein K\"ahler surfaces having some specific additional properties, and construct new examples.

The paper studies the quantum action for the five-dimensional real φ^3-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed.

A set of infinitesimal {rm Virasoro_{,L}}rm Virasoro_{,R} diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of `Wald-Zoupas' counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c_L=c_R=12J. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.

We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio R |eE|/m (R being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.

We introduce Einstein Fields, a neural representation that is designed to compress computationally intensive four-dimensional numerical relativity simulations into compact implicit neural network weights. By modeling the metric, which is the core tensor field of general relativity, Einstein Fields enable the derivation of physical quantities via automatic differentiation. However, unlike conventional neural fields (e.g., signed distance, occupancy, or radiance fields), Einstein Fields are Neural Tensor Fields with the key difference that when encoding the spacetime geometry of general relativity into neural field representations, dynamics emerge naturally as a byproduct. Einstein Fields show remarkable potential, including continuum modeling of 4D spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use. We address these challenges across several canonical test beds of general relativity and release an open source JAX-based library, paving the way for more scalable and expressive approaches to numerical relativity. Code is made available at https://github.com/AndreiB137/EinFields

Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and non-existence pieces of C.

We allow the Higgs field Phi to interact with a dilaton field chi of the background spacetime via the coupling chi^2,Phi^daggerPhi. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to chi. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on chi, we present an textit alternative mechanism: the Higgs VEV will be used to construct Planck's constant hbar and speed of light c. Specifically, each open set vicinity of a given point x^* on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of hbar_* and c_* per hbar_*proptochi^{-1/2}(x^*) and c_*proptochi^{1/2}(x^*), causing these ``fundamental constants'' to vary alongside the dynamical field chi. Moreover, in each open set around x^*, the prevailing value chi(x^*) determines the length and time scales for physical processes occurring in this region as lproptochi^{-1}(x^*) and tauproptochi^{-3/2}(x^*). This leads to an textit anisotropic relation tau^{-1}propto l^{-3/2} between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of c along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lema\^itre redshift relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa through a declining speed of light in an expanding Einstein--de Sitter universe, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the H_0 tension without requiring a dynamical dark energy component.

We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlargers the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.

We study the inflationary phenomenology of a rescaled Einstein-Gauss-Bonnet gravity. In this framework, the gravitational constant of the Einstein-Hilbert term is rescaled due to effective terms active in the high curvature era. Basically, the total theory is an F(R,G,phi) theory with the Gauss-Bonnet part contributing only a non-minimal coupling to the scalar field, so it is a theory with string theory origins and with a non-trivial F(R) gravity part. The F(R) gravity part in the high curvature regime contributes only a rescaled Einstein-Hilbert term and thus the resulting theory is effectively a rescaled version of a standard Einstein-Gauss-Bonnet theory. We develop the formalism of rescaled Einstein-Gauss-Bonnet gravity, taking in account the GW170817 constraints on the gravitational wave speed. We show explicitly how the rescaled theory affects directly the primordial scalar and tensor perturbations, and how the slow-roll and observational indices of inflation are affected by the rescaling of the theory. We perform a thorough phenomenological analysis of several models of interest and we show that is it possible to obtain viable inflationary theories compatible with the latest Planck data. Also among the studied models there are cases that yield a relatively large blue tilted tensor spectral index and we demonstrate that these models can lead to detectable primordial gravitational waves in the future gravitational wave experiments. Some of the scenarios examined, for specific values of the reheating temperature may be detectable by SKA, LISA, BBO, DECIGO and the Einstein Telescope.

We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed à la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamiołkowski correspondence and develop a Cholesky algorithm for bi-partite systems. This enables a canonical construction of adjoint actions which recover the behaviour of the original CP-maps. Our results hold under separability assumptions and the requirement that the maps are completely bounded and preserve the subideal of finite rank operators.

In this paper, we investigate the quantum behaviour near the classical singularity of a black hole. We describe the black-hole interior by the Kantowski-Sachs metric, with a string propagating in this region. This approach is motivated by the fact that, near the classical singularity, spacetime curvature reaches Planck or string scales, necessitating a description in terms of string-theoretic degrees of freedom. The string dynamics is formulated via the Polyakov action, and the combined system is canonically quantized to derive the corresponding Wheeler-DeWitt equation. Although the equation is separable in the radial and azimuthal string sectors, the remaining geometric and string degrees of freedom are nontrivially coupled. To address this, we employ a perturbative approach and obtain the wave function up to first order. At the zeroth-order, the angular part is described by the general Heun function, while the geometric part is expressed in terms of the Bessel function. The first-order wave function is governed by a source term containing the zeroth-order solution, and we obtain its explicit expression in terms of the complementary function and the particular integral. We confirm regularity of the wave function at both zeroth and first order, at the singularity as well as at the horizon. Regularity at the horizon imposes a discretization condition on one eigenvalue, while another eigenvalue is quantized due to the azimuthal periodicity of the wave function. Importantly, both zeroth- and first-order solutions satisfy the DeWitt boundary condition, implying resolution of the black hole singularity within this quantum framework.

Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short distances; interaction of photons with the graviton background leading to the important cosmological consequences; the time delay of photons due to interactions with gravitons; deceleration of massive bodies in the graviton background which may be connected with the Pioneer anomaly and with the problem of dark matter.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra Cl(0,6). The resultant rich geometric structure can be leveraged to establish a combined framework of the standard model and gravity, wherein a gravi-weak interaction between the extended vierbein field and the extended weak gauge field is allowed. In conjunction with the composite Higgs model, we examine the vierbein field as a Cooper-pair-like fermion-antifermion condensation. Quantum gravity is realized indirectly via the quantized standard model spinor fields which underlie the composite space-time metric. We propose that the fundamental energy scales of the universe including the Planck scale are emergent and resulted from quantum condensations, thus possibly addressing the cosmological constant problem through an unconventional multi-scale renormalization procedure for multiplications of divergent Feynman integrals. The Clifford algebra approach also permits a weaker form of charge conjugation without particle-antiparticle interchange, leading to a Majorana-type mass that conserves lepton number. Additionally, with reshuffling the traditional quark-lepton pairing pattern of three generations of fermions, we explore a three-Higgs-doublet model with Higgs VEVs 246 GeV, 42 GeV and 2.5 GeV which could explain the mass hierarchies of fermions.

We classify equivariant C^*-actions on moduli spaces of Higgs bundles corresponding to the Painlevé equations. Using this, we compute the Floer-theoretic filtrations on the cohomology of these spaces, introduced by Ritter and the second author in arXiv:2304.13026. We compare it with the ``P=W'' and the filtration obtained by multiplicities of the irreducible components of the nilpotent cone, ultimately deducing that the Floer-theoretic filtration coincides with the multiplicity filtration, for all 2-dimensional Higgs moduli.

We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature T_D=1/(πα), where 2α is the temporal extent of the diamond. The regulated Gibbons--Hawking--York contribution gives I_D^E=-A_0/(4G), with A_0 the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy--area relation S_D=A_0/(4G). For weak matter perturbations crossing a localized portion of the future horizon, a Raychaudhuri analysis relates the associated Killing-energy flux to the area response, yielding a local physical-process first law at leading order near the bifurcation surface and, for classical matter satisfying the null energy condition, a local second law. Uniform conformal surface gravity establishes the zeroth law, while zero temperature is approached only in the limit αtoinfty, in which the finite causal horizon disappears. These results show that a coherent horizon-law structure can arise within a causal diamond, a fundamental building block of the causal structure of Minkowski spacetime. The derivation is explicit in (2+1) dimensions, while the physical results retain the same form for spherical causal diamonds in dgeq3.

In this work, we propose an effective action of the two-dimensional conformal field theory for the Soft modes appearing in Quantum ElectroDynamics (QED) in 4 dimensions. This is motivated in two ways. First, we motivate the notion of an effective action for the Soft modes using the path integral formalism. Second, by noting the transformations of the on-shell gauge-fixed QED action, we deduce necessary boundary conditions and the corresponding form of the counter-terms that govern the IR sector. We review a derivation of the Soft Ward-Takahashi identity using path integral methods and offer an alternative derivation that follows from the large-gauge variations of the QED action. Because our effective action is that of a conformal theory, we calculate the relevant central charge.

We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the G_N^3 terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature Bern:2019nnu,Damour:2019lcq. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in Bern:2019nnu or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to Bern:2019nnu, but not to Damour:2019lcq. This implies that we also agree on all observables with Bern:2019nnu to the sixth post--Newtonian order to G_N^3.

The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon, known as gravitational lensing, has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known as Einstein ring. This model has recently allowed the measurement of the mass of a star, the white dwarf Stein 2051 B. The purpose of this work is to show an accessible and uptodate introduction to the effect of gravitational lensing, focused on the Einstein ring and the measurement of the mass of Stein 2051 B. The intended audience of this article are non-graduate students of physics and similar fields of study, and requires only basic knowledge of classical physics, modern physics, algebra and trigonometry.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

Spacetime singularities displayed by classical black hole solutions are expected to be cured by high-energy effects, beyond the regime of validity of General Relativity. On the other hand, there are well-known examples of classical theories allowing for nonsingular black hole solutions. The most prominent is obtained by complementing the gravitational sector of General Relativity with a minimally coupled nonlinear-electrodynamics sector. It has recently been shown that purely electric/purely magnetic nonsingular black holes in an Einstein-nonlinear-electrodynamics setup are always plagued by a gradient instability. In this work, we derive the quadratic action for linear perturbations of static, spherically symmetric dyonic solutions of Einstein-nonlinear-electrodynamics theories with a general dependence on both invariants. We show that regularity of the center, absence of ghosts and angular gradient stability cannot hold simultaneously: arbitrarily close to a regular center, at least one photon polarization has a negative squared angular propagation speed. We further show that regularity drives one electromagnetic kinetic eigenvalue to zero at the center, which may limit perturbative control near the core. Evading the obstruction requires extending the theory, for example by introducing additional degrees of freedom.

We investigate gravitational-wave echoes in a horizonless compact object model, a non-perturbative solution of the semi-classical Einstein equation that reproduces the entropy-area law from the bulk structure. By employing a model of anisotropic fluids in classical general relativity (GR), we show that odd-parity gravitational waves are not reflected at the object's surface but are trapped inside due to the exponentially strong redshift, and that the echo-delay time extremely exceeds the age of the Universe. Consequently, the echo signals are effectively unobservable, which is consistent with current null results from echo searches. We finally discuss how this quantum black hole and the conventional classical black hole could be distinguished observationally.

In this work, we embark on the thermodynamic investigation concerning a family of primary charged black holes within the context of shift and parity symmetric Beyond Horndeski gravity. Employing the Euclidean approach, we derive the functional expression for the free energy and derive the first thermodynamic law, offering a methodology to address the challenge of extracting the thermal quantities in shift-symmetric scalar tensor theories characterized by linear time dependence in the scalar field. Following the formal analysis, we provide some illustrative examples focusing on the thermal evaporation of these fascinating objects.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A simple set-up based on Einstein-dilaton gravity indicates that the vicinity of the phase transition is governed by a linear-dilaton CFT. Employing this CFT we calculate scaling of observables near T_c, and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. We show that the second speed of sound vanishes at the transition also with the mean field exponent.

We determine the quadrupolar logarithmic tidal response of electrically charged Einstein-Euler-Heisenberg black holes from the coupled static odd-parity gravitational and electromagnetic equations. Although the second electromagnetic invariant vanishes on the electric background, its quadratic interaction contributes to the axial fluctuation equations. At first order in the Euler-Heisenberg coupling a, a direct asymptotic recursion gives the canonical running matrix C_{rm can}^{rm EH}=(9aQ^2/10)left(smallmatrix0&-Q-Q&Msmallmatrixright), defined as the coefficients multiplying the canonical source vector in the r^{-2}log(r_0/r) term. The resulting local coefficients retain the full dependence on the subextremal ratio Q{M} at this perturbative order. The two quartic invariants partially cancel in both nonzero channels, while the action-normalized fields make gravitoelectromagnetic reciprocity explicit. The local extremal limit of the running matrix reproduces the corresponding two-invariant effective-field-theory result after convention conversion. Allowing independent quartic couplings further shows that identical electric background geometries can have different axial running matrices and yields algebraic inverse relations within the specified two-operator model. The calculation determines local logarithmic running within minimally coupled quartic electrodynamics; the finite horizon-matched response requires an additional global matching calculation.

Given a Finsler manifold (M,F) and suitable nested regions B_1subset B_2subset B_3, with Msetminus B_1 connected and non-contractible, as in the model case of concentric balls in mathbb R^n, ngeq2, we consider conformal deformations φ_λF which can be chosen so as to leave F unchanged outside B_3 and grow on B_2setminus B_1. This growth creates an energy barrier, diverging with λ, that low-energy curves cannot cross. The minimax families can therefore be chosen in the path space of Msetminus B_1, which contains compact subsets of arbitrarily large category. Consequently, for every minmathbb N and all sufficiently large λ, there exist at least m geodesics joining two prescribed points, all avoiding B_1. This extends to the Finsler setting an idea of Capozzi, Fortunato and Greco. The same scheme applies to Randers metrics α+β, with α deformed and β unchanged, as well as to fixed-energy trajectories of non-relativistic electromagnetic systems and relativistic Lorentz-force trajectories, and light rays in spacetimes endowed with a causal Killing field. In the non-relativistic case only the scalar potential is perturbed, while the magnetic field is preserved. When the Killing field is not everywhere timelike, the Fermat principle yields a possibly singular Randers--Kropina metric on a spacelike hypersurface. Under a natural admissible category condition, combining localized barriers with Randers approximation gives m Randers--Kropina geodesics with pairwise distinct lengths, equivalently m future-pointing light rays with pairwise distinct arrival times.

Adopting general frameworks for quantum-classical dynamics, we analyze the interaction between quantum matter and a classical gravitational field. We point out that, assuming conservation of momentum or energy, and assuming that the dynamics obeys Hamiltonian formalism or a particular decomposition property set out in the paper, the classical gravitational field cannot change the momentum or energy of the quantum system, whereas the quantum gravitational field can do so. Drawing upon the fundamental relationship between conservation laws and the quantum properties of objects, our analysis offers new perspectives for the study of quantum gravity and provides a novel interpretation of existing experimental observations, such as free fall.

The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group.

The mean Hawking flux does not determine how quantum stress fluctuations perturb a black-hole geometry. That information resides in field correlations, including vacuum contributions absent from the outgoing luminosity. Here we connect the complete exterior Unruh Wightman function to a finite-band stochastic reconstruction of Schwarzschild geometry. We retain the incoming vacuum and both outgoing frequency branches, form the connected stress covariance before angular projection, and propagate its monopole through a density-driven radial response. A shared Gaussian reconstruction then resolves how the value and derivative of the lapse control different geometric observables. For the specified covariance and noise amplitude, 2,200 realizations give relative widths of 0.0185 for the local horizon radius and 0.0483 for the surface-gravity temperature parameter, consistently across histograms and reconstruction checks. Covariance derivatives explain this unequal sensitivity. The construction separates the quantum-state input from the gravitational closure and spatial sampling assumptions, providing a reproducible finite-resolution description of how Hawking-field correlations affect horizon positions and surface-gravity statistics.

Recently, Fernandes discovered an analytic solution for rotating black holes in semiclassical gravity induced by the trace anomaly. These solutions exhibit some distinctive characteristics, including a non-spherically symmetric event horizon and violations of the Kerr bound. As a crucial assumption to uphold causality in spacetime, we investigate the validity of the weak cosmic censorship conjecture (WCCC) within this class of solutions with type-A trace anomaly by introducing a test particle on the equatorial plane. Our study reveals three distinct mechanisms that can potentially destroy the event horizon, leading to a violation of the WCCC. Our findings indicate that, with the exception of extremal Kerr, static extremal, and static singular black holes, the WCCC may be violated under the first-order perturbation of the test particle. These results suggest the need for further exploration of modifications to the behavior of the test particle under quantum effects in order to address the violation of the WCCC in this system.

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral I(N,α) for arbitrary loop geometries, directly improving upon recent AI-assisted attempts BCE+25 that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials C_l^{(3/2)} to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for I(N,α) at large N that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.

We present the analytic evaluation of the gravitational energy and of the angular momentum flux with tidal effects for inspiraling compact binaries, at next-to-next-to-leading post-Newtoian (2PN) order, within the effective field theory diagrammatic approach. We first compute the stress-energy tensor for a binary system, that requires the evaluation of two-point Feynman integrals, up to two loops. Then, we extract the multipole moments of the system, which we present for generic orbits in center-of-mass coordinates, and which are needed for the evaluation of the total gravitational energy and the angular momentum flux, for generic orbits. Finally, we provide the expression of gauge invariant quantities such as the fluxes, and the mode amplitudes and phase of the emitted gravitational wave, for circular orbits. Our findings are useful to update earlier theoretical studies as well as related phenomenological analyses, and waveform models

The static tidal Love numbers of black holes vanish in general relativity (GR), but are generically non-zero, and in fact 'run' logarithmically with scale, in more general theories or beyond the static limit. We expose a model-agnostic framework for the running of Love numbers at the dynamical level, valid for any tidal perturbation on any static, spherically symmetric, asymptotically flat background, based on the near-zone expansion in powers of the frequency ω and on the monodromy at spatial infinity. A master recurrence formula determines the monodromy generator to all orders in ω^2, whose three independent entries fully encode the running of the Love numbers. This structure explains the quadratic nature of the renormalization group equation, here proved to all orders and for any type of Love number. We discuss the scheme dependence of the logarithmic coefficients, which is made transparent by the monodromy form. In particular, this clarifies that the anomalous exponents of the tidal field, the so-called 'renormalized angular momentum' of the Mano-Suzuki-Takasugi formalism, are scheme-invariant and directly computable on any spacetime, without need of explicit solutions. We discuss several applications to black holes, including the derivation of a closed-form formula for the leading dynamical running of axial Love numbers of Reissner-Nordström black holes, proving in particular that it vanishes in the extremal limit. For generic black holes beyond GR, we prove that dynamical running probes deformations of the metric at lower multipoles than the static one, and we illustrate the power of the method by deriving some exact results for the Hayward and Bardeen regular black holes.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

We formulate a new class of modified gravity models, that is, generalized four-dimensional Chern-Pontryagin models, whose action is characterized by an arbitrary function of the Ricci scalar R and the Chern-Pontryagin topological term {}^*RR, i.e., f(R, {}^*RR). Within this framework, we derive the gravitational field equations and solve them for a particular model, f(R, {}^*RR)=R+β({}^*RR)^2, considering two ansatzes: the slowly rotating metric and first-order perturbations of Gödel-type metrics. For the former, we find a first-order correction to the frame-dragging effect boosted by the parameter L, which characterizes the departures from general relativity results. For the latter, Gödel-type metrics hold unperturbed. We conclude this paper by displaying that generalized four-dimensional Chern-Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: Φ, a dynamical degree of freedom, while the second, vartheta, a non-dynamical degree of freedom. In particular, the scalar field vartheta emerges coupled with the Chern-Pontryagin topological term {}^*RR, i.e., ^*RR, which is nothing more than Chern-Simons term.

Between 1972 and 1975, Jacob Bekenstein proposed that black holes possess entropy proportional to their horizon area, and Stephen Hawking derived this relationship from semiclassical quantum field theory in curved spacetime, predicting thermal radiation from black holes. These developments established black hole thermodynamics as a formal framework connecting general relativity, quantum mechanics, and statistical physics. However, this synthesis rests on approximations whose validity remains unproven in regimes where quantum gravitational effects become important. This article provides a detailed overview of the historical development from 1972 to 1975 and surveys modern proposals, such as the holographic principle and gravitational path integrals. We highlight persistent theoretical challenges, including the information paradox, the trans-Planckian problem, backreaction effects, and the absence of experimental verification. The work concludes by identifying which aspects of black hole thermodynamics are well-established and which remain speculative or fundamentally incomplete.

A complete theory of null Cartan normal helices in Minkowski space-time E^4_1 is developed. Two algebraic conditions, obtained by successive differentiation of the helix invariant along a unit C-constant normal field, fully characterize null Cartan helices; the quadratic condition yields two mutually orthogonal helix axes in the Lorentzian metric. Special field types are analyzed and null Cartan cubics are shown to be normal helices. On a timelike hypersurface, a Darboux frame with six curvature functions is constructed from first principles, the normal isophotic condition is shown to reduce to a linear first-order ODE, and the existence of normal silhouettes in E^4_1 is established.

The binding energies of the five bound rotational levels J=0-4 in the highest vibrational level v=14 in the X^1Sigma_g^+ ground electronic state of H_2 were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H_2S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F^1Sigma_g^+ - X^1Sigma_g^+ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The s-wave scattering length of the H + H system is derived from the binding energy of the last bound J=0 level via a direct semi-empirical approach, yielding a value of a_s = 0.2724(5) a_0, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the malpha^4 relativity contribution to a_s was found to be significant. In a similar manner a value for the p-wave scattering volume is determined via the J=1 binding energy yielding a_p = -134.0000(6) a_0^3. The binding energy of the last bound state in H_2, the (v=14, J=4) level, is determined at 0.023(4) cm^{-1}, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed.

Reduction in effective spacetime dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wavefunction factors depend nontrivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a "covert" pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

The Kramers-Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

We revisit Hawking's original derivation of the evaporation process in a non-stationary spacetime, presenting it in a clear and pedagogical manner, with a focus on the spherical collapse of a star into a black hole. Our analysis highlights the underlying assumptions in the calculations, clarifying their physical significance, potential implications, and the limitations of this approach.

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.

Let G be a Lie group equipped with commuting left and right linear representations on a vector space V, and let GJoin V be the associated centered semidirect product. We develop a reduction scheme for covariant field theories on principal bundles with structure group GJoin V from both Lagrangian and Hamiltonian perspectives, obtaining the reduced Euler-Poincaré and Lie-Poisson field equations decomposed into their mathfrak g- and V-components, where mathfrak g is the Lie algebra of G. We also derive the reduced multisymplectic form formula, as well as the Noether and energy-momentum balance laws. Our reduction results are compared with those for principal bundles with standard semidirect-product structure groups, and the role of the centered variables is investigated: they retain the original two-sided geometric data and separate the left and right contributions via the heart and diamond operators. The framework is then applied to a two-sided matrix microstructural model and to the second-order jet group on mathbb R^r, G_r^2. For the matrix model, the conjugation representation decomposes Mat(3) into scalar, vector, and symmetric-traceless sectors, clarifying its precise relation to director and alignment-tensor variables without identifying it with standard nematodynamics. For the one-dimensional jet group on a (1+1)-dimensional Minkowski base, we obtain a semilinear symmetric-hyperbolic system and an exact traveling conversion front with explicit energy-momentum exchange between the linear- and quadratic-jet sectors. Its hyperbolic-target interpretation yields a conserved positive energy for the linearized perturbations. A nonlinear numerical experiment illustrates the reduced evolution and reconstruction of the group-valued field, with consistency assessed through mesh refinement and an independent wave-map computation.

This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the star-exponential with the quantum propagator for bosonic systems, this work develops the analogous extension for the fermionic case. A rigorous method, based on Grassmann variables and coherent states, is constructed to obtain a closed-form expression for the fermionic star-exponential from its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, allowing for the calculation of the ground state energy directly in phase space. Finally, the method is validated by successfully applying it to the simple and driven harmonic oscillators, where it is demonstrated that a simplified ("naive") approach (with an ad-hoc "remediation") is a valid weak-coupling limit of the rigorous ("meticulous") formalism, thereby providing a new and powerful computational tool for the study of fermionic systems.

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic monopoles, rigid body mechanics, and quantum information theory. This expository article presents an introduction to the Hopf fibration that is accessible to undergraduate students. We use the algebra of quaternions to illustrate algebraic and geometric properties of the Hopf fibration and the connection with rotations of 3-space that is the basis for natural applications to physics and engineering.

In this Essay, we will look at the relation between the No Transmission principle and the Strong cosmic censorship (SCC), which we will highlight in the background of quantum gravity. We show that taking quantum gravity into account, one can provide a complete picture of the instability of the inner horizon and the principle that two independent CFTs, under the gauge-gravity duality, imply that the dual bulks must also be independent in that there must not exist a way to transmit a signal between the two spacetimes. We show that this can simply be interpreted as SCC, and that the inner horizon must be unstable (at either linear or nonlinear orders) to be in accordance with holographic quantum gravity.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

A new class of solutions describing the composition of compact stars has been proposed, assuming that the fluid distribution inside the star is anisotropic. This is achieved by assuming the appropriate metric potential and then solving Einstein's field equations using Karmarkar conditions [Karmarkar K. R., Proc. Indian Acad. Sci. 27 (1948) 56] to derive the expressions for star density, the radial and tangential pressures in terms of the constants A, B, a paramter `a' and the curvature parameter R. The equations thus obtained have been passed through rigorous conditional analysis. It is further shown that the model is physically viable and mathematically well-behaved, fulfilling the requisite conditions viz., regularity condition, strong energy condition, causality condition, etc. Observed star candidates including EXO 1785-248, SMC X-1, SAXJ1808.43658(SS2), HER X-1, 4U 1538-52, Cen X-3 and LMC X-4 were found to conform to a good approximation through the outcome of this model for a=0.5.

For every integer Nge4, we construct a fixed smooth, non-locally-conformally-flat metric on the n-dimensional unit sphere S^n for which the constant Q_{2N}-curvature equation admits an L^infty-unbounded sequence of positive solutions. The construction applies for nge2N+20 when N=4,5, nge2N+19 when 6le Nle8, nge2N+18 when 9le Nle17, and nge2N+17 when Nge18. For each L in N cup {0}, the metric can be chosen arbitrarily close to the round metric in the C^L norm. Together with the known cases N=1,2,3, this establishes noncompactness at every order, with dimension bounds that we expect to be optimal. We derive an explicit formula for the fixed-volume Hessian of total Q_{2N}-curvature in transverse-traceless (TT) directions at closed Einstein metrics satisfying Ric=(n-1)g. Building on Juhl's formulas, we identify this Hessian, for every NinN and n>2N, as a degree-N polynomial in the Lichnerowicz Laplacian. For the metric perturbations generated by algebraic Weyl tensors in the construction, the quadratic reduced energy with fixed bubble center is a positive multiple of this Hessian restricted to a four-dimensional TT space. Differentiation with respect to the bubble scale then yields a finite matrix whose exact sign analysis establishes the required indefiniteness in the stated dimension ranges. After continuation to real n, this matrix changes from negative definite to indefinite at n_N=2N+a_*+c_*N^{-1}+O(N^{-2}) as Ntoinfty, with a_*approx16.201871 and c_*approx13.512880, explaining the eventual bound nge2N+17.

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of {rm w}_{1+infty}, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''S algebra,'' the gauge-theoretic analog of {rm w}_{1+infty}. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

For finite nilpotent groups J and N, suppose J acts on N via automorphisms. We exhibit a decomposition of the first cohomology set in terms of the first cohomologies of the Sylow p-subgroups of J that mirrors the primary decomposition of H^1(J,N) for abelian N. We then show that if N rtimes J acts on some non-empty set Omega, where the action of N is transitive and for each prime p a Sylow p-subgroup of J fixes an element of Omega, then J fixes an element of Omega.

We argue that the celestial conformal field theory exhibits patterns of a logarithmic conformal field theory. We uncover a Jordan block structure involving the celestial stress tensor and its logarithmic partner, a composite operator built from the stress tensor and the Liouville field. Using a limiting process whose parameter corresponds to the infrared cut-off of gravity, we perform some basic consistency checks, particularly the calculation of two-point correlators, which reveals the expected logarithmic behavior. We comment on the vanishing value of the central charge in the celestial conformal field theory and explain how the logarithmic partner is relevant for its well-behavedness.

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho{rmr}ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

The dynamics of Einstein-conformally coupled Higgs field (EccH) system is investigated near the initial singularities in the presence of Friedman-Robertson--Walker symmetries. We solve the field equations asymptotically up to fourth order near the singularities analytically, and determine the solutions numerically as well. We found all the asymptotic, power series singular solutions, which are (1) solutions with a scalar polynomial curvature singularity but the Higgs field is bounded (`Small Bang'), or (2) solutions with a Milne type singularity with bounded spacetime curvature and Higgs field, or (3) solutions with a scalar polynomial curvature singularity and diverging Higgs field (`Big Bang'). Thus, in the present EccH model there is a new kind of physical spacetime singularity (`Small Bang'). We also show that, in a neighbourhood of the singularity in these solutions, the Higgs sector does not have any symmetry breaking instantaneous vacuum state, and hence then the Brout-Englert-Higgs mechanism does not work. The large scale behaviour of the solutions is investigated numerically as well. In particular, the numerical calculations indicate that there are singular solutions that cannot be approximated by power series.

In this work we investigate neutron stars (NS) in f(R,L_m) theory of gravity for the case f(R,L_m) = R + L_m + sigmaRL_m, where R is the Ricci scalar and L_m the Lagrangian matter density. In the term sigmaRL_m, sigma represents the coupling between the gravitational and particles fields. For the first time the hydrostatic equilibrium equations in the theory are solved considering realistic equations of state and NS masses and radii obtained are subject to joint constrains from massive pulsars, the gravitational wave event GW170817 and from the PSR J0030+0451 mass-radius from NASA's Neutron Star Interior Composition Explorer ({it NICER}) data. We show that in this theory of gravity, the mass-radius results can accommodate massive pulsars, while the general theory of relativity can hardly do it. The theory also can explain the observed NS within the radius region constrained by the GW170817 and PSR J0030+0451 observations for masses around 1.4~M_{odot}.

Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its role in the dynamics of systems and hinders any formulation to merge quantum mechanics with general relativity, specifically when considering quantum gravity. To overcome those limitations, several authors tried to construct an operator which is conjugate to the Hamiltonian of quantum systems implementing some essential features of the relativistic time. These formulations use the concept of internal or intrinsic time instead of the universal coordinate time used in textbooks. Furthermore, recently it is remarked that the consideration of time with relativistic features could enhance the analysis techniques in quantum information processing and have an impact on its status in causal orders and causal structures of quantum information. The role of clocks, their accuracy and stability has become an important issue in quantum information processing. This article present a substantiative review of recent works which reflect the possibility of utilizing quantum time, measured by quantum clock devised according to Page-Wootters scheme, to stand as a resource for quantum information processing.

We derive bounds on the lifetime of an evaporating black hole. The bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. We use the recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and we find a lower bound on the purification time of the black hole, which scales as M_0^4/hbar^{3/2}, where M_0 is the initial black hole mass. Additionally, motivated by quantum gravity considerations, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, we find that the the purification time is extended to be exponential in the square of the initial black hole mass, i.e. in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant which releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

In a novel application of the tools of topological data analysis (TDA) to nonperturbative quantum gravity, we introduce a new class of observables that allows us to assess whether quantum spacetime really resembles a ``quantum foam" near the Planck scale. The key idea is to investigate the Betti numbers of coarse-grained path integral histories, regularized in terms of dynamical triangulations, as a function of the coarse-graining scale. In two dimensions our analysis exhibits the well-known fractal structure of Euclidean quantum gravity.

The large-D membrane paradigm provides a perturbative, non-gravitational description of black hole dynamics. While the local second law of thermodynamics has been established for neutral membranes, the explicit determination of the local entropy production equation within the charged large-D membrane framework remains unsolved. In this paper, we compute the subleading-order correction to the divergence of the membrane velocity for a charged black hole in a flat background. We evaluate the corresponding scalar Einstein-Maxwell constraint equation at the physical event horizon via the non-affine null Raychaudhuri equation, and relate the physical horizon expressions to the auxiliary membrane kinematics, demonstrating that the membrane velocity produces a non-negative divergence at the first non-vanishing order in the membrane worldvolume, which is driven by two quadratic forms: the membrane shear and a novel contribution generated purely by the Maxwell field. Using this result, we construct the membrane entropy current and prove that its divergence is non-negative through this order, thereby establishing the local second law for the charged large-D membrane paradigm.

Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in the collision of massless Dirac fermions. Time in the relativistic many-body state should evolve while maintaining the direction of time in each particle, even if the particles are viewed from any inertial frames. This kinematical requirement leads to spontaneous symmetry breaking in the vacuum of these states, which gives a different meaning to the results of the Higgs model. In this vacuum, massless fermion-antifermion pairs and coherent collection of gauge bosons condense, which determine each other's mass. When a local excitation of the condensed gauge bosons propagates in space, a Higgs-like boson appears. The effective coupling of this Higgs-like boson to gauge bosons is calculated as a one-loop process. With this coupling, the total cross section of the pair annihilation of fermion and antifermion to gauge boson pair is calculated. Renormalizability of this model is discussed using the inductive method. Since the Higgs Lagrangian is not assumed, the divergence we must renormalize is only the logarithmic divergence, not the quadratic one.

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group G acts transitively on a space M, any G-invariant function on a product space X times M can be reduced to an invariant of the isotropy subgroup H of M acting on X alone. Our approach establishes an explicit orbit equivalence (X times M)/G cong X/H, yielding a principled reduction that preserves expressivity. We apply this characterization to Equivariant Neural Fields, extending them to arbitrary group actions and homogeneous conditioning spaces, and thereby removing the major structural constraints imposed by existing methods.

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type J on a punctured sphere. We denote the AD theories as (J^b[k],Y), where J^b[k] and Y represent an irregular and a regular singularity respectively. We restrict to the `minimal' case where J^b[k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra W^{k_{2d}}(J,Y), where k_{2d}=-h+ b{b+k} with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b=h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

The study of continuous spin particles, as general low-energy implications of relativity and quantum mechanics, has intensified in recent years with potential experimental signatures. In this note we show that these particles are absent in perturbative super-string theories, generalising a result in arXiv:1302.4771 to the supersymmetric case. This stands out as a general low-energy prediction of all perturbative superstring constructions.

We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces of dimension d-2 with constant curvature and analyse in detail the field equations and manifest their symmetries. The field equations of the full system are shown to reduce to a single or couple of ODE's which can be used to solve analytically or numerically the theory for the symmetry at hand. Further solutions can also be generated by a solution generating technique akin to the EM duality in the absence of a cosmological constant. We then find and analyse explicit solutions including black holes and gravitating solitons for the case of four dimensional relativity and the higher-dimensional oxydised 5-dimensional spacetime. The general solution is obtained for a certain relation between couplings in the case of cylindrical symmetry.

The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of the AKSZ formalism where the target spaces are differential graded contact manifolds. We show that the space of fields inherits a weak contact structure, and we construct a solution to the analogue of the classical master equation, defined via the Jacobi bracket. In the n=1 case, we recover the Jacobi sigma model, and in the n=2 case, we obtain three-dimensional topological field theories associated to Courant-Jacobi algebroids.

The Shadowing Principle of Manin has proved a valuable tool for addressing questions of quantitative topology raised by Gromov in the late 1900s. The principle informally provides a way for bounded algebraic maps between differential graded algebras to be translated into nearby genuine maps between their geometric realizations. We extend this principle to finite towers of principal K(G,n) fibrations, and in particular apply this construction to nilpotent spaces. As a specific application of the extended principle, we provide upper bounds on the asymptotic behavior of volumes of nullhomotopies of Lipschitz maps into nilpotent spaces. We further refine these bounds in the case when c = 1 to nearly meet those of the simply connected setting. We similarly refine these bounds in the event the target space is coformal, and demonstrate that the bounds in this setting are nearly sharp.

In the present paper we study the singularity structure of the exterior field of neutron stars with the aid of the four-parameter exact solution of the Einstein-Maxwell equations. The complete analysis of this problem in the generic case becomes possible due to the implementation of the novel analytical approach to the resolution of the singularity condition, and it shows the absence of the ring singularities off the symmetry axis in the positive mass case, as well as the possibility of the removal of the ring singularity by a strong magnetic field in the negative mass case. The solution takes an extraordinarily simple form in the equatorial plane, very similar to that of the Kerr solution, which makes it most suitable for astrophysical applications as the simplest model of a rotating magnetized deformed mass. It also provides a nontrivial example confirming a recent claim that the varphi component of the electromagnetic four-potential has features inconsistent with the intrinsic properties of the electrovac metric, while the magnetic field is represented correctly by the t component of the dual electromagnetic four-potential.

E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves - waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass-proportional to a3 in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Whittaker potential theory also offers a simple explanation for expansion of the universe - it is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space.

We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau three-folds. We introduce the moduli space of multi-curves and show how it leads to invariants. Our construction is based on an idea of Witten. In the special case that each connected component of the Lagrangian submanifold has the rational homology of a sphere we define rational numbers F_{g,h} for each genus g and h boundary components.

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar single particle states/operators, there should be multiparticle operators appearing in the celestial OPE. We extend the existing flat-space dictionary by constructing composite primaries from both Carrollian and Celestial perspectives. In the process, we demonstrate some subtleties in deriving the Poincaré primary condition from the Carrollian limit, clarify the compatibility of principal series representations with highest weight representations and unitarity in Celestial CFT, and discuss how the celestial OPE block expansion emerges from a 2D CFT standpoint.

Modifying the fundamental commutation relation of quantum mechanics to reflect the influence of gravity is an important approach to reconcile the contradiction between quantum field theory and general relativity. In the past two decades, researchers have conducted extensive research on geometric phase problems in non-commutative spaces, but few have mentioned the correction of geometric phase problems using the Generalized Uncertainty Principle (GUP). This paper is the first to study the phase correction of Aharonov-Bohm (AB) effect by GUP.

We study the inverse adjoint problem for a perturbative bosonic outgoing map. Within the polynomial bosonic canonical-commutation-relation (CCR) algebra, we prove a constructive integrability theorem: order-by-order preservation of the CCRs is sufficient to reconstruct recursively a formal self-adjoint generator whose exponential implements the outgoing map by adjoint conjugation. At each order, the Baker--Campbell--Hausdorff contribution determined by previously reconstructed generators is subtracted from the outgoing coefficient, and the remaining homogeneous CCR conditions determine the next generator explicitly. We apply the construction to graviton scattering in the null-surface formulation (NSF), specialized to the flat solution-space sector with Minkowski metric, null generators, affine parameter, and cone measure. The NSF outgoing map preserves the Ashtekar radiative CCRs through (δa_3), corresponding to order (\varepsilon^2). At this order, the scalar CCR sector uniquely selects the symmetric ordering (c=1) for the nontrivial interacting kernel. The associated linear contraction, generated by the same cubic kernel, cancels the double-contraction contribution from ([δa_2,δa_2^\dagger]). The theorem then reconstructs the self-adjoint generators (δT_1) and (δT_2), providing a formal perturbative unitary implementation. The resulting canonical organization also separates the direct (2\to2) contribution into irreducible-loop, one-particle-reducible, and factorized sectors.

In an earlier paper [arXiv:2511.03669] we extracted the OPE of celestial CFT operator duals of positive helicity graviton and scalar particles from the Mellin transformed relevant MHV amplitudes of conformal gravity, realised as the bosonic subsector of the Berkovits-Witten theory. A soft theorem analysis of bulk MHV amplitudes established that this conformal gravity exhibits a chiral bms_4 symmetry on the celestial sphere with the associated sl(2,R) current algebra, which acquires a non-trivial central extension, unlike the Einstein gravity. Here we construct a 2d chiral CFT free-field realisation of the relevant chiral bms_4 algebra in terms of three free scalars (ϕ_i) and three (β_i,γ_i) ghost pairs, and propose vertex operators for the positive-helicity graviton primary G^{++}_Δ(z,z) as well as the scalar primary Φ_Δ(z,z), and compute their OPEs. These OPEs reproduce exactly those obtained from the bulk conformal gravity MHV amplitudes, providing a concrete celestial dual description of its MHV sector.

We study the dynamics of gravitons in a squeezed vacuum state in a thermal radiation background. Unlike traditional treatments that rely on the Boltzmann equation, we employ the Heisenberg equation and average it over general quantum states. In contrast to the usual Boltzmann-based descriptions, our approach captures the subtleties arising from quantum coherence in different number eigenstates, which is essential for soft graviton modes in the squeezed vacuum state. Our new method successfully reproduces the previous one-loop results within the in-in formalism when the expansion parameter is small and deviates significantly as the parameter increases, indicating that our results extend beyond the one-loop in-in formalism. We examine the implications of graviton emission effects stimulated by quantum coherence in both flat and expanding backgrounds. In the flat background, it is found that backreaction of radiation on the spacetime dynamics is crucial for significant stimulated emission. In the expanding background, to avoid the subtleties associated with superhorizon modes, we investigate the effect of emission within the horizon immediately after reheating and find a significant effect. We examined the IR graviton evolution from a symmetry perspective and propose a regularization prescription to eliminate the secular growth problem.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling A(phi) and chameleon/Vainshtein screening, we map cosmological responses {mu(z,k),Sigma(z,k)} inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials Phi_N. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with |gamma-1|simfewtimes 10^{-6}, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization {V(phi),A(phi)}. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters gamma,beta; and dot G/G) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, |gamma-1|lesssim (2-5)times 10^{-6} (Ka-/X-band or optical Shapiro), eta_{EEP}sim (1--10)times 10^{-17} (drag-free AIS), |dot G/G|sim(3-5)times10^{-15},yr^{-1} (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and (3-10)times improved ULDM-coupling reach from clocks. For a conformal benchmark, mu_{ lin,0}=0.10 implies chisimeq mu_{lin,0/2} and a Sun thin shell Delta R/Rlesssim (1/3chi)|gamma-1|/2=2.4times 10^{-3} at |gamma-1|=5times 10^{-6}; Vainshtein screening at 1 AU yields |gamma-1|lesssim 10^{-11}, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

The ideal magnetohydrodynamic (MHD) system that governs a conducting plasma---the Maxwell equations together with the conservation laws of mass, momentum and energy---is the same local balance structure that describes hot accretion flows around black holes. We introduce a uniform four-dimensional spacetime dilation \[ Φ_L:\;(t',x',y',z')\mapsto (t,x,y,z)=(Lt',Lx',Ly',Lz'),\qquad L>1, \] and show that it is a smooth, orientation-preserving C^infty diffeomorphism of flat spacetime. Pulling the MHD conservation laws back through Φ_L, we prove that the closed ideal-MHD system is form-invariant (covariant), with the current density rescaling as bm j=bm j'/L, the magnetic diffusivity as η'=η/L, and external sources rescaled by L. The transformation realises three physically distinct effects on the perturbed flow: a linearization to the tangent-space (linearised MHD) system, a movie slow-motion dilation of dissipative and dynamical timescales, and an electron-microscope magnification of small-scale structure. Taking the formal limit Ltoinfty localises the dynamics on a neighbourhood of a horizon: resistivity vanishes, the asymptotic time derivative freezes, and all transient multipolar structure of the infalling plasma redshifts away. The remaining stationary, axisymmetric, asymptotically flat electrovacuum is uniquely the Kerr--Newman geometry, so that the exterior of the compact object is characterised only by its mass M, angular momentum J and charge Q. The result provides a local, conservation-law-based perspective on the black hole no-hair theorem that is complementary to the classical Israel--Carter-- Robinson theorems and to contemporary gravitational-wave and Event Horizon Telescope tests.

In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in arXiv:hep-th/0402135 for which we provide the first explicit examples in Calabi-Yau orientifold compactifications with discrete fluxes below their respective tadpole constraint. As a proof of concept, we study the degree 18 hypersurface in weighted projective space CP_{1,1,1,6,9}. Furthermore, we look at 10 additional orientifolds with h^{1,2}=2,3. We find several flux vacua with hierarchical suppression of the vacuum energy with respect to the gravitino mass. These solutions provide a crucial stepping stone for the construction of explicit de Sitter vacua in string theory. Lastly, we also report the difference in the distribution of W_0 between supersymmetric and non-supersymmetric minima.

We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the super-inflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts CMB observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the Big-Bang Observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO).

In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.

Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures.

Whilst most of the binary configurations in modified theories of gravity are studied under quasi-circular orbit limit, eccentricity effects could play a significant role in future gravitational wave detections. We derive the gravitational radiation-reaction force for nonspinning eccentric orbits within the effective-one-body (EOB) description for the massless scalar-tensor theories up to 1.5 post-Newtonian (PN) order. The effects in such theories start at 1/c^3 and interestingly, the 1.5PN order effect is due to the radiation reaction square effects which is a conservative effect. The results derived here can be implemented in the quasi-circular EOB-based waveform models to construct waveform templates for generic orbit binaries within massless scalar-tensor theories of gravity.

We investigate Einstein-Gauss-Bonnet (EGB) 4D massive gravity coupled to nonlinear electrodynamics (NED) in an Anti-de-Sitter (AdS) background and find an exact magnetically charged black hole solution. The metric function was analyzed for different values of massive gravity parameters. We verified the first law of black hole thermodynamics and the generalized Smarr formula, treating the cosmological constant as thermodynamic pressure. Vacuum polarization is defined as the conjugate to the NED parameter. To analyze the local stability of the black hole, we compute specific heat. We investigated the Van der Waals-like/reentrant phase transition of the black holes and estimated the critical points. We observed small/large black hole (SBH/LBH) and small/intermediate/large black hole (SBH/IBH/LBH) phase transitions. The Joule-Thomson coefficient, inversion, and isenthalpic curves are discussed. Finally, the minimum inversion temperature and the corresponding event horizon radius are obtained using numerical techniques.

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

In the momentarily comoving frame of a cosmological fluid, the determinant of the energy-momentum tensor (EMT) is highly sensitive to its pressure. This component is significant during radiation-dominated epochs and becomes naturally negligible as the universe transitions to the matter-dominated era. Here, we investigate the cosmological consequences of gravity sourced by the determinant of the EMT. Unlike Azri and Nasri, Phys. Lett. B 836, 137626 (2023), we consider the most general scenario in which the second order variation of the perfect-fluid Lagrangian does not vanish. We analyze the dynamics of the power-law case and explore the cosmological implications of the scale-free model characterized by dimensionless couplings to photons and neutrinos. We show that, unlike various theories based on the EMT, the present setup, which leads to enhanced gravitational effects of radiation (EGER), does not alter the time evolution of the energy density of particle species. Using current cosmological observations, we constrain the model parameters and show that EGER may offer a viable mechanism for alleviating the Hubble tension. Although it exhibits a phenomenological analogy to tightly-coupled relativistic fluid scenarios, EGER remains purely gravitational in origin and yields distinguishable signatures in the small-scale anisotropies of the cosmic microwave background. The radiation-gravity couplings we propose here are expected to yield testable cosmological and astrophysical signatures, probing whether gravity distinguishes between relativistic and nonrelativistic species in the early universe.

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyze electromagnetic wave propagation on a quantum Robertson-Walker space time and show that Lorentz Invariance is not preserved. The formalism developed can be applied to the case where back reaction effects on the metric due to the electromagnetic field are taken into account, leading to non covariant field equations.

We derive a set of recursion relations for the perturbative evaluation of the scattering of two black holes in Einstein gravity. To illustrate, we solve the equations up to third post-Minkowskian order in the gravitational coupling constant G, recovering the correct result, including the back-reaction from gravitational radiation.

Through use of the Pauli-Villars regulator procedure we construct a second- plus fourth-order-derivative theory of gravity that serves as an ultraviolet completion of standard second-order-derivative quantum Einstein gravity that is ghost-free, unitary and power counting renormalizable.

Singular regular points often arise in differential equations describing physical phenomena such as fluid dynamics, electromagnetism, and gravitation. Traditional numerical techniques often fail or become unstable near these points, requiring the use of semi-analytical tools, such as series expansions and perturbative methods, in combination with numerical algorithms; or to invoke more sophisticated methods. In this work, we take an alternative route and leverage the power of machine learning to exploit Physics Informed Neural Networks (PINNs) as a modern approach to solving ordinary differential equations with singular points. PINNs utilize deep learning architectures to approximate solutions by embedding the differential equations into the loss function of the neural network. We discuss the advantages of PINNs in handling singularities, particularly their ability to bypass traditional grid-based methods and provide smooth approximations across irregular regions. Techniques for enhancing the accuracy of PINNs near singular points, such as adaptive loss weighting, are used in order to achieve high efficiency in the training of the network. We exemplify our results by studying four differential equations of interest in mathematics and gravitation -- the Legendre equation, the hypergeometric equation, the solution for black hole space-times in theories of Lorentz violating gravity, and the spherical accretion of a perfect fluid in a Schwarzschild geometry.

The observation of the shadow of the supermassive black hole M87^{*} by the Event Horizon Telescope (EHT) is sensitive to the spacetime geometry near the circular photon orbit and beyond, and it thus has the potential to test general relativity in the strong field regime. Obstacles to this program, however, include degeneracies between putative deviations from general relativity and both the description of the accretion flow and the uncertainties on "calibration parameters", such as e.g. the mass and spin of the black hole. In this work, we introduce a formalism, based on a principal component analysis, capable of reconstructing the black hole metric (i.e. the "signal") in an agnostic way, while subtracting the "foreground" due to the uncertainties in the calibration parameters and the modelling of the accretion flow. We apply our technique to simulated mock data for spherically symmetric black holes surrounded by a thick accretion disk. We show that separation of signal and foreground may be possible with next generation EHT-like experiments.

The composition gamma circ eta of Jordan curves gamma and eta in universal Teichm\"uller space is defined through the composition h_gamma circ h_eta of their conformal weldings. We show that whenever gamma and eta are curves of finite Loewner energy I^L, the energy of the composition satisfies $I^L(gamma circ eta) lesssim_K I^L(gamma) + I^L(eta), with an explicit constant in terms of the quasiconformal K of \gamma and \eta. We also study the asymptotic growth rate of the Loewner energy under n self-compositions \gamma^n := \gamma \circ \cdots \circ \gamma, showing limsup_{n rightarrow infty} 1{n}log I^L(gamma^n) lesssim_K 1, again with explicit constant. Our approach is to define a new conformally-covariant rooted welding functional W_h(y), and show W_h(y) \asymp_K I^L(\gamma) when h is a welding of \gamma and y is any root (a point in the domain of h). In the course of our arguments we also give several new expressions for the Loewner energy, including generalized formulas in terms of the Riemann maps f and g for \gamma which hold irrespective of the placement of \gamma on the Riemann sphere, the normalization of f and g, and what disks D, D^c \subset \mathbb{C} serve as domains. An additional corollary is that I^L(\gamma) is bounded above by a constant only depending on the Weil--Petersson distance from \gamma$ to the circle.

In this paper, we first study the consequence of spacetime translations and Lorentz transformations on Celestial CFT OPEs. Working with the light transforms of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincaré symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in Carrollian CFTs. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in d=3 dimension at the level of correlation functions in the near coincident limit.

This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski space. This construction is in contrast to the often used, non-smooth BMS transformations that appear in a gauge-fixed description of the theory.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

In this paper we construct the canonical harmonic coordinates of the Kerr metric within the multipolar post-Minkowskian (MPM) formalism to the fourth post-Minkowskian (4PM) order. Based on the well known Geroch--Hansen moments of Kerr metric and Gürsel's theorem, we derive the exact canonical MPM moments M_L,S_L, which are free of any gauge moments. With these moments, we iteratively compute the gothic metric perturbation h^{μν}_{can} up to 4PM order and compute the 4PM canonical metric g_{μν}^{can}. The resulting spatial and time components of these metrics are even functions of the spin parameter a while the mixed components are odd. This parity property distinguishes the canonical coordinates from other harmonic coordinates. To contrast this minimal-gauge construction, we also extract the 1PM source moments of the Kerr metric in the Jiang--Lin coordinates. We find that the Jiang--Lin representation possesses non-vanishing gauge moments starting from the 1PM order, whereas in the canonical representation gauge moments vanish to all orders. This comparison highlights the canonical coordinates as the most gauge-pure representation of the Kerr metric in the MPM framework. The complete canonical metric for the Schwarzschild case is also computed to all PM orders. A recent independent construction by Damgaard et al. using momentum-space recursion yields 4PM equivalent results expressed as a power series in a, providing a cross-validation of our closed-form 4PM canonical metric. The coordinate transformation linking the canonical Kerr coordinates to previously known harmonic Kerr coordinates remains an open problem.

We introduce and describe tt GrayHawk, a publicly available Mathematica-based tool designed for the efficient computation of gray-body factors for spherically symmetric and asymptotically flat black holes. This program provides users with a rapid and reliable means to compute gray-body factors for massless fields with spin \(s = 0, 1/2, 1, 2\) in modes specified by the angular quantum number \(l\), given a black hole metric and the associated parameter values. tt GrayHawk is preloaded with seven different black hole metrics, offering immediate applicability to a variety of theoretical models. Additionally, its modular structure allows users to extend its functionality easily by incorporating alternative metrics or configurations. This versatility makes tt GrayHawk a powerful and adaptable resource for researchers studying black hole physics and Hawking radiation. The codes described in this work are publicly available at https://github.com/marcocalza89/GrayHawk.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9-year data release from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. We set upper limits for a GWB from supermassive black hole binaries under power law, broken power law, and free spectral coefficient GW spectrum models. We place a 95\% upper limit on the strain amplitude (at a frequency of yr^{-1}) in the power law model of A_{rm gw} < 1.5times 10^{-15}. For a broken power law model, we place priors on the strain amplitude derived from simulations of Sesana (2013) and McWilliams et al. (2014). We find that the data favor a broken power law to a pure power law with odds ratios of 22 and 2.2 to one for the McWilliams and Sesana prior models, respectively. The McWilliams model is essentially ruled out by the data, and the Sesana model is in tension with the data under the assumption of a pure power law. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. We then place the most stringent limits so far on the energy density of relic GWs, Omega_gw(f),h^2 < 4.2 times 10^{-10}, yielding a limit on the Hubble parameter during inflation of H_*=1.6times10^{-2}~m_{Pl}, where m_{Pl} is the Planck mass. Our limit on the cosmic string GWB, Omega_gw(f), h^2 < 2.2 times 10^{-10}, translates to a conservative limit of Gmu<3.3times 10^{-8} - a factor of 4 better than the joint Planck and high-l CMB data from other experiments.

An important question in binary black hole mergers is to connect properties of the remnant black hole to those of the two initial black holes. These properties include not only the final mass and spin of the remnant, but also higher multipoles and answers to other questions such as, for a given initial configuration, which quasi-normal modes of the final black hole are excited, and what are the amplitudes of these modes? Such questions have thus far been primarily addressed through a study of the emitted gravitational wave signal. In this paper we consider a different alternative, namely using quasi-local black hole horizons themselves to establish the link between the initial and final states. Recent work has elucidated the behavior of black hole horizons in a merger. Cusps forming in such otherwise smoothly evolving horizons have been shown to play a central role in connecting the two initially separate black holes with the final remnant. In the present work, we will discuss from a numerical perspective how such cusps form in detail for the head-on collision of two non-spinning black holes. We show how the mass and higher mass multipole moments behave at the cusp and suggest a phenomenological model.

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.

Calculating the action and the interaction Hamiltonian at higher orders in cosmological perturbation theory is a cumbersome task. We employ the formalism of EFT of inflation in models of single field ultra slow-roll inflation and obtain a non-perturbative result for the Hamiltonian in terms of the Goldstone field pi. To complete the dictionary, a non-linear relation between the curvature perturbations and pi is presented. Equipped with these non-linear results, we calculate the higher order loop corrections in USR models which are employed for PBHs formation. It is shown that the loop corrections on long CMB scales increase rapidly with the number of loop L and the setup will go out of perturbative control at the four-loop level.

In the present work, we study the dynamical evolution of an homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to an homogeneous and isotropic NC Friedmann-Robertson-Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor a(t) and the two parameters beta_pm (t), which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe.

In this long paper we give a fairly complete analysis of outer billiards on the Penrose kite. Our analysis reveals that this 2-dimensional non-compact system has a 3-dimensional compactification, a certain polyhedron exchange map, and that this compactification has a renormalization scheme. These two features allow us to make some sharp statements concerning the distribution, large-scale geometry, fine-scale geometry, and hidden algebraic symmetries of the orbits. For instance, one of our results is that the union of the unbounded orbits has Hausdorff dimension 1. We give a computer-aided proof of the results concerning the compactification and the renormalization. This proof involves finitely many calculations done with exact integer arithmetic.

This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of w_{1+infty} on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators.

We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in R^3 can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological structure of real-projective 3-space.

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, (varepsilon,d,σ_0), a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity ν=pm1/2 and the Berry phase γ=π for loops encircling the EL, while ν=0 and γ=0 for those do not encircle the EL. Through matrix perturbation theory, we prove that the ε-pseudospectrum contour size scales as ε^{1/q} at an EP, where q is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear ε scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

In this manuscript we set up the direct and inverse scattering problems for step-like traveling-wave solutions of the nonlinear Schrödinger equation. Specifically, we consider initial data u(x,0) satisfying u(x,0)to u_0^ell(x) as xto-infty and u(x,0)to u_0^r(x) as xto+infty, where u_0^ell(x) and u_0^r(x) are elliptic traveling waves. Under suitable assumptions on the initial data we formulate the direct scattering problem and establish analytic properties of the scattering data. We then formulate the inverse problem as a Riemann--Hilbert problem and prove its solvability. Finally, we observe that this Riemann--Hilbert formulation is a special case of the one arising for full soliton-gas initial data.

We investigate in more detail the holographic model of a superconductor recently found by Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101, 031601], which is constructed from a condensate of a charged scalar field in AdS_4-Schwarzschild background. By analytically studying the perturbation of the gravitational system near the critical temperature T_c, we obtain the superconducting coherence length proportional to 1/1-T/T_c via AdS/CFT correspondence. By adding a small external homogeneous magnetic field to the system, we find that a stationary diamagnetic current proportional to the square of the order parameter is induced by the magnetic field. These results agree with Ginzburg-Landau theory and strongly support the idea that a superconductor can be described by a charged scalar field on a black hole via AdS/CFT duality.