Papers

We construct a finite-Hilbert interacting quantum model in which matter and geometric response are generated by a single Schwinger functional along one spatial refinement. Two inequivalent discretizations converge analytically to the same Hamiltonian on a fixed physical Fourier band, with second- and fourth-order regulator bounds. The common limit determines the excitation gap, connected nonlinear matter response, mixed matter-geometry susceptibility, and low-frequency geometric kernel. Within a prescribed covariant two-derivative FLRW sector, the latter fixes a positive induced Newton coefficient without an additional normalization parameter. The same spectral data define a conserved excitation stress and a regulator-stable semiclassical Friedmann trajectory. These results establish a common regulator limit for interaction, response, and backreaction within one microscopic family. The construction is restricted to a two-mode Fourier band, a finite oscillator cutoff, and a prescribed semiclassical gravitational sector; an interacting all-band quantum field theory with dynamical geometry is not constructed here.

In the present paper, the cases of a uniformly accelerated reference frame and a Schwarzschild black hole in two and four dimensions are discussed focusing on formal aspects of the corresponding quantum scalar field theories. The main emphasis is made on building consistent quantum field theories and highlighting the problems that are not considered elsewhere. In particular, some pathologies in the case of a uniformly accelerated reference frame are discussed in detail: it is shown that some quantum states that are well defined in Minkowski spacetime possess an infinite energy when considered in Rindler spacetime. In the case of a Schwarzschild black hole in four dimensions, it is shown that the standard theory providing the Unruh vacuum state turns out to be inconsistent. The problem of consistency of quantum scalar field theory in Kruskal-Szekeres spacetime is also discussed.

Gravitational-decoupling provides a systematic framework for constructing black hole geometries from known (seed) solutions (such as the Schwarzschild), whose exterior properties closely resemble those of the seed solution while still retaining potentially distinguishable features. Using this approach, we study a class of static, spherically symmetric hairy black holes and examine how such deformations affect their horizon structure, photon spheres, shadow scales, and scalar quasinormal modes (QNMs). We first determine the physically controlled regions of the parameter space by imposing the relevant horizon and energy condition requirements, while retaining configurations outside these domains only for exploratory comparison. To isolate geometric effects, we compare solutions at a common horizon radius, while accounting explicitly for the distinction between the mass parameter entering the seed geometry and the ADM mass measured asymptotically. The resulting ADM normalized shadow scales are used for an illustrative comparison with the characteristic angular scales of M87* and Sgr A*. We also compute massless scalar QNMs using the sixth-order Wentzel-Kramers-Brillouin approximation and the improved Asymptotic Iteration Method, finding close agreement over the modes considered. Our results show that fixing the horizon radius does not uniquely determine either the optical or perturbative properties of the spacetime, and that mass normalization can significantly alter the interpretation of geometric trends. Horizon structure, null geodesic observables, and scalar QNMs therefore provide complementary probes of gravitationally-decoupled black hole geometries.

At a deeper level the principle of least action is interpreted as the law of least entropy increase consistent with Prigogine's principle of minimum entropy production, and the implications of quasistatic information quantization rule (Proc. R. Soc. A 480: 20240024), are explored for the conjectured second law of quantum complexity. It is thus shown that the conjectured second law of complexity is derivable from the information quantization rule such that long after heat-death the quantum state complexity evolves as $C(t)=C_{\rm max}\exp(-1/t)$, increasing with time to a saturation value $C_{\rm max}$ that is exponential in the equilibrium entropy $S_{\rm max}$. For the out-of-equilibrium circumstances, however, the quantum complexity can decrease with the time, asymptotically tending to a minimum determined by the distance from equilibrium.

We study cosmological perturbations in multi-field inflation in which the scalar fields couple to the Gauss-Bonnet terms through a general coupling function $f(\phi^a)$. We derive the complete quadratic action for the field perturbations in spatially flat gauge and find that, besides corrections to the kinetic, gradient and mass matrices, the Gauss-Bonnet coupling induces an antisymmetric velocity coupling that vanishes in Einstein gravity. Decomposing the field perturbations into curvature and isocurvature modes, we show that the effective mass of the curvature perturbation and the non-derivative mixing mass vanish identically, $\mathcal{M}_{\mathcal{R}}^2 = \mathcal{M}_{\rm mix}^2 =0$ which are justified by the Weinberg's adiabatic mode. We then compute the curvature power spectrum in two limits. First, when the isocurvature mode is heavy, it can be integrated over all scales. This yields an effective single-field theory of the curvature perturbation with a modified sound speed. Second, when the gradient of the coupling function is aligned with the background trajectory ($f_N =0$), the derivative mixings disappear and the superhorizon transfer of isocurvature into curvature perturbations is governed by the turn rate, which is modified by the Gauss-Bonnet corrections. We also present the tensor power spectrum and the tensor-to-scalar ratio at linear order in the coupling.

We provide a geometric foundation for the kinetic theory of photons. Although the induced metric $\hat h$ on the light cone bundle $\Gamma_0^+$ is degenerate, which causes the corresponding volume element to vanish, we can still use a method similar to the Hodge dual to construct a volume element $\eta_{\Gamma_0^+}$ for the light cone bundle. Based on this geometric structure $(\Gamma^+_0,\eta_{\Gamma_0^+},\hat h)$, we establish the fully covariant Boltzmann equation for photons. More importantly, the volume element and the induced metric are linked in a nontrivial way, which allows the physical distributions to be defined consistently. This yields the corresponding hydrodynamic quantities and their divergences, which take the same form as in the case of massive particles.

We investigate the Joule-Thomson expansion of a non-commutative Schwarzschild-AdS black hole, whose space-time geometry is described by the Lie-algebraic $\kappa$-deformed space-time, and show that the $\kappa$-deformation parameter induces Joule-Thomson expansion in an uncharged-AdS black hole. We find the ratio of minimum inversion temperature to critical temperature $T_i^{(min)}/T_c \simeq 0.493$, is independent of the deformation parameter, and is in close agreement with the value for Reissner-Nordstrom black hole. Furthermore, we show the existence of a minimum black hole mass (depending on the $\kappa$-deformation parameter) below which the Joule-Thomson expansion vanishes.

We study the one-loop relation between an effective-field-theory extension of Poincaré gauge theories of gravity with propagating torsion and its unimodular counterpart. In the Einstein representation, we consider two representative quadratic torsion subsectors, namely totally antisymmetric (axial) torsion and the vector component of hook-antisymmetric torsion. On maximally symmetric metric backgrounds with vanishing background torsion, the diffeomorphism-invariant and genuine unimodular theories yield identical one-loop determinants in both sectors, reproducing the same local logarithmic divergences. We further examine flat backgrounds with homogeneous axial or vector torsion, where metric-torsion mixing is present. In each case, the torsion-dependent one-loop effective action in unimodular gauge and in the genuine unimodular formulation is controlled by the same physical determinant. Thus, for the actions and backgrounds considered, the unimodular constraint does not modify local one-loop torsion dynamics. We also delineate the limitations of this equivalence and the extensions needed for generic torsionful curved backgrounds.

We derive the rank-two string-Carroll limit of the canonical stress–spin Ward system for probe matter on a fixed torsion-free background. Beyond rank-one Carroll spin hydrodynamics, this retains the coupled Riemann–spin force, a second longitudinal momentum projection, and the longitudinal boost bivector allowed only by a two-dimensional longitudinal kernel. We first extract the term linear in an independent spin amplitude $\varsigma$ and then expand in the near-horizon parameter $\lambda=\epsilon^2$, avoiding contamination by the omitted $\mathcal{O}(\varsigma^2)$ thermodynamic spin feedback. For finite mixed stress and $S^{\lambda\mu\nu}=\mathcal{O}(\varsigma\epsilon^p)$, $p=0$ is the unique sector in which the induced stress and curvature source balance at the first generic Ward order. On the regular branch of a smooth nonextremal static spherical outer horizon, locally normalized longitudinal and transverse spin amplitudes obey the same dilution law, while the curvature force first appears at $\mathcal{O}(\varsigma\lambda^2)$. For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family $p=\alpha\mathcal E+\Pi$, $0\leq\alpha<1$, we obtain an explicit closed-form parametric solution, leading profiles for both spin channels, and fixed-radius, linear-spin corrections to enthalpy, pressure, and rapidity away from the sonic point. The response is governed by $\mathcal R^{(L)}_h=(f_2+3f_1\psi_1)/2$ and the longitudinal spin flux. We prove that the stationary closed-sphere Killing flux is invariant under regular pseudo-gauge improvements. In Reissner–Nordström, the response vanishes at the radial-tidal inversion $|Q|/M=2\sqrt{2}/3$; in the Einstein–Maxwell–dilaton family, its zero is $R_-/R_+=(1+a^2)/2$ for $0\leq a<1$. The Frenkel limit removes this response and the longitudinal boost sector.

We comment on an error in the charged quark star literature ( Phys. Rev. D, 102(3):034031, 2020 ) that resulted in erroneous solutions to the radial stability equations for charged interacting quark stars in ( Phys. Rev. D, 104(12):123007, 2021 )[2]. In this comment article we recalculate the fundamental radial eigenfrequencies for charged, interacting quark stars in general relativity and discuss any departure from previous results [2]. Most of the qualitative trends persist, but the magnitudes of the separation between the maximum mass and stability points on a given branch can change significantly. We also note that all branches in [2] that contained no stable solutions now have stable solutions in their corrected counterparts. The net effect is that in all of the studied cases charged quark stars have a greater range of stability than originally predicted. We also compare four recent observational constraints not included in previous studies, and find that these constraints are satisfied by a subset of the mass-radius relations we obtain.

In particle physics the virtual N$^3$LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. For gluon-fusion $gg\!\to\!H$ we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the $\overline{\mathrm{MS}}$ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit $E_M\!\to\!\infty$.

This work represents an initial step towards a systematic framework for identifying hidden symmetries in algebraically general (Petrov type I) spacetimes. Motivated by this, we focus on Weyl's class, which provides a simple yet a class of algebraically general solutions of static, axisymmetric geometries. Employing the canonical forms of rank-2 Killing tensors, we systematically derive the constraints that must be satisfied for these spacetimes to admit genuine hidden symmetries. Our analysis yields an analytical characterization of the obstructions to integrability within subclasses of Weyl's class, both in vacuum and electrovacuum. In particular, we find that no two-Killing-vector member of Weyl's class, in vacuum or electrovacuum, admits an irreducible Killing tensor capable of supplying the additional integral of motion required for complete integrability. Members of Weyl's class admitting a third additional Killing-vector isometry (i.e. Levi-Civita) are already completely integrable through their manifest symmetries alone admitting only reducible Killing tensors. This result provides an analytic complement to previous analytical and numerical investigations, and establishes a systematic connection between the absence of hidden symmetries and the breakdown of complete integrability. Beyond the specific classification obtained here, these results demonstrate the potential of our approach regarding the canonical forms of Killing tensor as a systematic tool for probing hidden symmetries in Petrov type I spacetimes.

We study supersymmetric near-horizon geometries of gauged $D=5$ supergravity coupled to vector multiplets, on the branch where the canonical rotational Killing vector $\tilde V$ of the cross-section ${\cal S}$ is non-vanishing. No rotational symmetry is assumed, and nothing about the set where the frame built from the Killing spinors degenerates. On a compact connected ${\cal S}$ without boundary a second rotational Killing field, independent of $\tilde V$, always exists and is an isometry of all of ${\cal S}$. Where the moduli vary it is $$ U_i=\parallel\eta_-\parallel^2\big(\alpha Z_i-\epsilon_{ijk}Z^ju^k\big) , \qquad u_i=\Phi P_i-h_i , $$ a polynomial in the horizon data, hence smooth everywhere; where the moduli are constant the horizon is locally homogeneous. The only further hypothesis for these results is that the superpotential $\Phi=\chi V_IX^I$ is nowhere zero — weaker than the non-negativity of the scalar potential assumed in the earlier literature. The two sub-branches are separated by $K=Q_{IJ}C^IC^J$, which vanishes exactly in the minimal theory: $K\equiv0$ recovers the result of Grover, Gutowski, Papadopoulos and Sabra, while elsewhere $K>0$ and $\alpha$ is either identically zero or nowhere zero. Each of $K\equiv0$, $P\equiv0$ and $P\not\equiv0$ occurs on compact ${\cal S}$. Constant moduli return the local geometries of Kunduri and Lucietti as a conclusion, not an ansatz. Varying moduli with $\alpha\not\equiv0$ give a cohomogeneity-one $T^2$ action whose orbit space is a closed interval, so ${\cal S}$ is $S^3$, a lens space or $S^1\times S^2$; the last is excluded by two global first integrals, a new one, $\alpha\parallel\eta_-\parallel^4$, and the constant spinor norm already known. A varying-moduli supersymmetric $AdS_5$ black ring therefore cannot exist with $\alpha\not\equiv0$; the $S^1\times S^2$ window survives only at constant moduli or at $\alpha\equiv0$.

We present a simple model with a n + 4-dimensional metric with compactified extra dimensions with a space dependent radius R. We show that changes in the profile of R are sourced by (visible) matter density and Newtonian potential. We can reproduce rotation curves of spiral galaxies and provide an expression for R. In order to test our hypothesis, we propose six experiments.

The Einstein Telescope (ET) is a proposed underground infrastructure in Europe to host future generations of gravitational-wave (GW) detectors. Two configurations are under investigation. The first is the two-site solution with an L-shape detector at each site similar to the LIGO configuration. The second configuration is the single-site triangular detector. While numerous analyses over the last decade have already proven that the distributed network of GW detectors is the scientifically preferred solution, it was also argued that the advantage might not be decisive enough to dismiss ET's triangle configuration. The modeling of aspects such as noise correlations in these configurations has only been treated superficially in the past. In this article, we introduce a time-domain simulation of environmental noises in the ET triangle using available data from ET's candidate sites. We simulate and analyze correlated environmental noise as well as coincident glitches produced by transients in the environmental fields. We find that these features pose an important limitation to the observational capabilities of the ET triangle and limit the utility of its null stream.

Superconducting cosmic strings (SCSs) are characterized by three parameters: the dimensionless string tension $G\mu$, the current amplitude $Y$, and the vector coupling, $\tilde{e}$ as recently explored in \cite{Rybak:2024our}. Using the Charge-Velocity-dependent One-Scale (CVOS) model, we compute the stochastic gravitational wave background (SGWB) emitted by current-carrying loops, including the suppression effect of vector radiation. While previous studies have shown that large $\tilde{e}$ suppresses the SGWB, allowing larger $G\mu$ to evade pulsar timing array (PTA) bounds \cite{Rybak:2024our}, we demonstrate that this parameter space is definitively constrained by an independent, astrophysically clean probe: the Dark Ages global $21$-cm signal. We recalculated the recently derived $21$-cm bounds \cite{Si:2025vsj} into the generic $(\tilde{e},Y,G\mu)$ parameter space and find that at the threshold where vector radiation emission starts dominating, any coupling $\tilde{e}\gtrsim 10^{-7}$ and $Y\simeq 0.67$ and $G\mu\gtrsim 10^{-13}$ injects sufficient ionizing radiation to completely erase the $21$-cm absorption signal at redshift $z\simeq89$. Greater current amplitudes impose more stringent constraints. This excludes a large parameter space considered viable. Our model-independent results highlight the complementarity between future lunar-based $21$-cm experiments and gravitational wave (GW) observatories.

We propose a thermodynamic description of the genuine Kerr-Bertotti-Robinson (Kerr-BR) black hole spacetimes. Contrary to previous studies, such solutions no longer have electric charge. Consequently, the thermodynamics is governed by simple relations. Namely, upon introducing a suitable normalization factor for the timelike Killing vector, these spacetimes are characterized by the standard Hawking temperature, Bekenstein's entropy, Komar mass and angular momentum, and horizon angular velocity. The corresponding mass is shown to obey the standard Christodoulou-Ruffini formula, along with the standard first law and Smarr relations. In fact, by a proper rescaling of coordinates and solution parameters, and up to a non-trivial parameter space constraint, we formally recover the thermodynamic quantities of the vacuum Kerr solution. This is used to bring the genuine Kerr-BR spacetime into a Kerr-like form.

Extreme mass-ratio inspirals (EMRIs) can magnify small departures from Kerr dynamics into appreciable gravitational-wave phase shifts accumulated over many orbital cycles. We exploit this sensitivity to investigate the imprint of a rotating black hole's acceleration on an EMRI waveform. The spinning C metric poses two obstacles to the standard Kerr flux framework: the spacetime is not asymptotically flat, and the acceleration breaks the reflection symmetry that supports exactly equatorial circular timelike orbits. For sufficiently small acceleration $AM$, we therefore formulate the calculation in an intermediate Kerr-like wave zone satisfying $M/r\ll1$ and $Ar\ll1$, and construct a near-equatorial circular orbit by examining its coupled radial–polar stability. We derive the separated point-particle source for the spin$-2$ radial Teukolsky equation, construct a regular normalized angular solution, solve the radial equation using the Sasaki–Nakamura transformation and the Green function method, and couple the resulting horizon and far-zone fluxes to the adiabatic evolution of stable near-equatorial circular orbits. The framework recovers the Kerr limit and reproduces the dominant $l=2$ Kerr fluxes with relative errors of order $10^{-7}$. Acceleration modifies both radiation reaction and the orbital frequency, producing a characteristic nonmonotonic accumulated dephasing. For $M=10^6M_\odot$, $m_s/M=10^{-5}$, $a/M=0.7$, and $AM=3\times10^{-7}$, the dominant-mode dephasing slightly exceeds $1$ rad over one year. Thus even weak acceleration can generate an order-radian secular phase imprint on long-duration EMRIs within the controlled regime of the present approximation.

Estimating spectral density matrices for future space-based gravitational-wave detectors such as LISA is challenging due to the long duration of the data and the correlated instrumental noise across multiple time-delay interferometry channels. In this work, we investigate a specialized mean-field stochastic gradient variational Bayes (SGVB) procedure for fast posterior approximation in long-duration multivariate spectral density estimation. Based on the existing eigenbasis representation of the blocked Whittle likelihood approach, the posterior model applies a Cholesky factorization to represent the inverse spectral density matrix and models the resulting frequency-dependent entries with cosine basis functions, with a discounted regularized horseshoe prior assigned to the basis coefficients. We test mean-field SGVB as a stand-alone posterior approximation by comparing it with Hamiltonian Monte Carlo (HMC) targeting the same posterior model. In simulation studies based on autoregressive and moving average processes, SGVB produces posterior median spectral estimates close to those obtained from HMC at substantially lower computational cost. We then apply the method to two one-year, fixed-delay, stationary, noise-only LISA simulations and show that the SGVB spectral density estimates are consistent with HMC and Welch estimates across the LISA analysis band, while requiring substantially less computation. These results demonstrate that SGVB provides a scalable Bayesian approach to spectral density estimation for long-duration multivariate LISA noise analysis.

We discuss the origin of the modes appearing at the Schwarzschild black hole horizon and decaying at integer multiples of the surface gravity. We argue that no excitations generated at the horizon by the plunging of a particle into a black hole can leave it. Our argument is based on the fact that, when the particle approaches the horizon, its speed is necessarily boosted to ultra-relativistic values and its near-horizon gravitational field becomes a Dray-'t Hooft shockwave, which is an exact, nonanalytic, and nonperturbative solution of Einstein's equations. The corresponding metric perturbations are localized at the horizon and can never reach a distant observer.

We obtain an exact dyonic black-hole solution in quadratic nonlinear electrodynamics defined by $-F+aF^{2}+bG^{2}$ on the special locus $b=a/2$. At this locus, the radial dependence in the electric constitutive relation cancels and the magnetic charge decouples, allowing the field equations to be integrated exactly. Using the field strength as the independent variable, we construct the solution in parametric closed form, with the radial quadrature expressed through Gauss hypergeometric functions and the cosmological constant retained. The solution recovers dyonic Reissner–Nordström–(anti-)de Sitter in the Maxwell limit, the known magnetic solution for vanishing electric charge, and the Euler–Heisenberg electric branch for vanishing magnetic charge. Its perturbative expansion agrees with the known dyonic result at first order and extends it to all orders. We find a three-horizon window requiring both electric and magnetic charges, while the corresponding Smarr integral is also expressed in closed hypergeometric form. The energy density and pressures are obtained analytically, showing that the electric charge enlarges the region satisfying the dominant energy condition relative to the purely magnetic case. Three distinct central curvature behaviors are identified, including a tuned self-energy singularity. We further develop the extended thermodynamics, treating the nonlinear coupling and pressure as thermodynamic variables, and find that the critical ratio decreases below the Maxwell value $3/8$ and disappears above a threshold coupling. Finally, birefringent photon propagation produces a split shadow doublet with a splitting of about $0.5\%$, whereas the geometric light ring and scalar ringdown are nearly insensitive to the nonlinear coupling, indicating that the main observable imprint of the nonlinearity lies in polarization-dependent photon propagation.

To leading order, the gravitational-wave (GW) signal from binary neutron stars depends on the individual spins, $\chi_1$ and $\chi_2$, only through the effective spin parameter $\chi_{\rm eff}$. We present the first systematic investigation of individual-spin effects on ejecta, $r$-process nucleosynthesis, and kilonova emission, including comparisons at fixed total mass, mass ratio and $\chi_{\rm eff}$. We use numerical relativity ejecta from three total mass regimes with the finite-temperature, composition-dependent SFHo equation of state and neutrino emission and absorption. For $M_{\rm tot}=2.55\,M_\odot$ at fixed $\chi_{\rm eff}=0$, individual spins change the dynamical ejecta mass by a factor of ${\sim}45$, while the absolute $A\geq140$ yield spans more than two orders of magnitude and the lanthanide to light $r$-process mass ratio increases from ${\sim}2$ to ${\sim}70$. Prompt-collapse $4.10\,M_\odot$ models show heavy-element yield differences exceeding four orders of magnitude at $\chi_{\rm eff}=0$. The kilonova retains the individual-spin imprint, with peak brightness differences reaching ${\sim}0.9$ mag. At $40\,{\rm Mpc}$, all three fixed $\chi_{\rm eff}=0$ pairs remain above adopted depths at common epochs for all viewing angles, with same-epoch colour differences reaching ${\sim}1.5$ mag. The colour imprint persists when the simulation-derived secular ejecta are replaced by the same parametric disc outflow, indicating that disc mass differences are not the primary driver and that dynamical ejecta make an important contribution. Neutrino absorption systematically brightens the kilonova and shifts peak-associated colours blueward. These EM signatures can break the degeneracy between individual spins in the GW signal.

We extend the finite-solid-angle general relativistic radiation transport method of C. J. White et al. (2023) to time-dependent spacetimes represented in ADM form. This Valencia-type solver retains the angular transport and local implicit matter coupling of the original HARM-type solver, but replaces its time-independent Kerr–Schild tetrad and conserved-variable normalization with an Eulerian formulation. A Cholesky-gauge spatial tetrad makes the frame and its derivatives algebraic functions of the ADM variables, providing smooth, metric-compatible angular transport. The resulting transport system couples directly to an evolving spacetime, agnostic to the gauge evolution equations. Our test suite, including flat and curved beams, radiation–fluid coupling, and time-dependent geometries, establishes the accuracy and robustness of this approach. We further apply the Valencia-type solver to a radiative circumbinary disk, illustrating its potential for multi-messenger studies of dynamical strongly gravitating systems.

The Stone-von Neumann theorem makes canonical quantization unique only after one imposes strong continuity of the Weyl translation groups. We show that this continuity assumption cannot be certified by any finite-resolution interrogation of the Weyl relations. A finite protocol probes only finitely many phase-space displacements and bounded expectation values, thereby determining a protocol algebra \(C_S\) generated by a finitely generated subgroup of Weyl translations, but not the regularity of an extension to the full Weyl algebra. Using the polymer representation as a canonical non-regular representation, we prove that for every regular Weyl representation, every normal state, and every finite family of bounded protocol observables, a polymer state reproduces the same expectation values to arbitrary prescribed accuracy. Thus finite agreement with Schrödinger quantum mechanics does not operationally certify the regularity hypothesis entering uniqueness. The result does not assert physical equivalence between regular and polymer quantizations, it identifies where additional input, such as Hamiltonian dynamics, energy regularity, semiclassicality, or a continuum limit, is required to distinguish or select representations. In this precise sense, non-regular polymer kinematics are not excluded by finite Weyl data alone, a point of direct relevance to quantum-gravity motivated quantizations.

We formulate a data-completeness test for extracting low-energy characteristic-cone running from flat-space on-shell renormalization-group residues. In four-dimensional, parity-even Einstein–scalar–Maxwell effective field theory through four derivatives and four external fields, Wilson directions are first placed on the physical EFT quotient and background propagation is represented by a traceless response on the full massless root sector. The response is identifiable from chosen amplitude coordinates precisely when the amplitude kernel lies in the response kernel. For the published opposite-helicity vector–scalar residue we find $\beta_\mu C_{\gamma\phi}^{(2)}=-55/(96\pi^2)$ and, after an order-reduced frame translation, the contribution $\beta_\mu(r_T-r_\gamma)=-55/(48\pi^2M_{\rm P}^4)$. A finite operator registry gives explicit rank-two incompleteness tests: independent $F^4$ directions split photon polarizations on a magnetic background, while $\mathcal CFF$ produces an analytic splitting along a principal Weyl axis on a Petrov-I Einstein–scalar background. For the isolated scalar–photon contact, direct Schur reduction finds nonzero raw mixing but no first-order physical off-diagonal entry, by the Maxwell Ward identity. Thus the residue fixes one diagonal cone contribution but does not determine the term-complete characteristic response over the declared admissible coefficient domain.

Computing boson star families traditionally requires repeated solution of nonlinear eigenvalue boundary-value problems and careful numerical continuation through turning points. We develop a physics-informed neural network (PINN) that learns the map from the physical parameters and radial coordinate directly to the scalar and metric fields over an equilibrium solution manifold. Regularity and asymptotic boundary conditions are incorporated into the network output, while the training objective combines pointwise supervision, Einstein-Klein-Gordon residuals, and curve-level constraints on the Arnowitt-Deser-Misner mass and Noether charge. A trained model generates a complete configuration in a single forward pass. Across representative one-, two-, and three-branch families, the method reconstructs the mass-frequency spirals and conserved quantities, including configurations on inner branches that require delicate continuation in conventional solvers. These results establish physics-informed surrogate learning as a practical route to amortized exploration of nonlinear self-gravitating solution families.

We study how discrete self-similarity (DSS) in the critical behavior of scalar-field collapse is imprinted on primordial-black-hole (PBH) mass functions. Using the DSS-modulated critical scaling law found in cosmological simulations, we propagate the near-threshold mass map into normalized PBH mass functions during a {kination} era. We compare Gaussian window function, $k$-space top-hat window function, and real-space top-hat window function, together with a real-space top-hat window function multiplied by a kination transfer function. We find that critical behavior in gravitational collapse produces an irreducible minimum width even for an infinitesimally narrow primordial spectrum. DSS then modulates this critical-scaling profile, generating approximately log-periodic features in mass. At fixed horizon mass, successive equal-phase points of the DSS-modulated critical mass map satisfy $\Delta\ln M_{\rm PBH}=\gamma P_{\rm ln}$. Consequently, in the narrow-spectrum limit, the corresponding structures in the final mass function are expected to satisfy $\Delta\ln m\simeq\gamma P_{\rm ln}$, or $m_{n+1}/m_n\simeq5.6$, for the fiducial Choptuik DSS parameters $\gamma$ and $P_{\rm ln}$. For broad primordial spectra, the convolution over horizon masses dephases the DSS pattern and progressively washes out the critical substructure. We normalize the mass functions so that we may primarily study the profile shape and the survival of DSS substructure, rather than the absolute PBH abundance. These results provide a bridge between cosmological DSS collapse simulations and PBH phenomenology including population observables.

A black hole need not ring down in isolation, since a nearby companion can subject it to an external gravitational tide. We calculate how a quadrupole tide modifies the Schwarzschild black hole resonances. Linearising the exact tidally distorted Schwarzschild solution in the tidal amplitude $A$, we derive the diagonal odd- and even-parity perturbation equations on the deformed background and compute the formal first order displacements of analytically continued Schwarzschild resonances. Each diagonal first order shift factorises as $\delta\omega_{n\ell m}=A\,c_{\ell m}\kappa_{n\ell}$, giving one reduced complex coefficient for each $(n,\ell)$, expressed as a ratio of contour integrals, multiplied by a universal Zeeman-like pattern that splits the $2\ell+1$ azimuthal multiplet. For the $\ell=2$ and $\ell=3$ sectors analysed explicitly, the odd- and even-parity shifts coincide, so Schwarzschild isospectrality survives at first order in the tidal amplitude. Quadratic tidal forces, by contrast, can break this degeneracy. Moreover, for a physical companion, the astrophysically dominant $(n,\ell,m)=(0,2,2)$ mode oscillates faster and decays more slowly. Finally, we show that the eikonal shifts admit a geometric description in terms of the Penrose limit about the tidally deformed photon ring.

The constancy of Newton's gravitational constant G is a fundamental prediction underlying general relativity and a critical assumption in theories of gravity beyond it. We report a high-precision test of a possible temporal variation of G in a strong gravitational field, using high-resolution ultraviolet spectra of Ni V absorption lines in the white dwarf G191-B2B obtained with the Hubble Space Telescope Imaging Spectrograph (HST/STIS). By comparing the measured line centroids with laboratory wavelengths and isolating the gravitational-redshift contribution, we obtain dG/G = (-0.014 +/- 0.016) x 10^-15 yr^-1 at a strong-field potential phi approximately 10^4, corresponding to an absorption redshift z_abs approximately 8.47 x 10^-5. The result is consistent with a constant G and places a stringent constraint on its secular variation in the strong-field regime. Our measurement demonstrates the potential of white-dwarf stars as a sensitive probe of temporal variations in the gravitational coupling.

With the observational accuracy of astrometric space telescopes such as Gaia, the Newtonian theoretical framework for positional astronomy is no longer appropriate. To model all effects relevant at the corresponding levels of accuracy, a more sophisticated description in the framework of General Relativity is required. It is generally known how various relativistic effects affect a given astrometric observation. In particular, the maximal light deflection of a given Solar System body can be easily estimated for a given observer. However, astrometric parameters for a given source are computed from a series of observations of that source. Depending on the relativistic effect, the fraction of observations affected, at some given level of accuracy, by that relativistic effect can vary and also be very small. Our goal is to investigate the impact of unaccounted relativistic effects on the astrometric parameters of a source observed by a Gaia-like astrometric telescope. The standard relativistic framework for Gaia is used to highlight such effects in some cases where they are most significant. Then, using the simulation tool AGISLab, we fit a set of Gaia-like observations of a given number of sources to the standard Gaia-like astrometric model for astrometric source parameters, but using different incomplete relativistic models. In this way we obtain the errors of the astrometric parameters if one were to drop different elements of the relativity model. A simplified analytical description of the errors is also provided and discussed. We demonstrate that, due to averaging over many observations per source, the errors in the astrometric parameters are drastically smaller than the corresponding relativistic effects in individual observations. This opens a way to potentially simplify the relativistic model for future astrometric projects aiming for higher accuracy than Gaia.