Papers

We develop a unified formulation of leading soft photon theorems for nondegenerate static spherical horizons. By fixing the photon mode normalization from the horizon symplectic form, we obtain a common angular soft factor whose sign follows from the boundary orientation. We determine the geometric coefficients in the local angular and momentum representations for a chosen radial normalization. The charge balance includes horizon endpoint data and contributions from other boundaries. This formulation brings black hole and cosmological horizons into a common description. Applying the same construction to Yang-Mills fields yields the corresponding tree-level soft gluon theorem. These results identify the common soft structure underlying different horizon geometries.

We investigate inflationary dynamics and isotropization in a phantom-field model with five families of potentials on Bianchi I, Bianchi III, and Kantowski-Sachs backgrounds. First, the general properties of the model are established, and Heusler's proposition is extended. To address the limitations of this proposition, a powerful dynamical-systems approach is then adopted to provide a comprehensive analysis of the cosmological evolution. In total, 87 critical points are identified and their properties are analyzed. Throughout the analysis, we emphasize the physical interpretation of the mathematical results and aim to provide a thorough explanation of the rationale behind the choice of each mathematical tool and variable. Within this framework, the conclusions of Collins and Hawking and of Burd and Barrow are revisited, and several challenging questions with deep conceptual implications are posed and discussed.

We derive the classical logarithmic soft graviton theorem for the scattering of massive particles in four-dimensional asymptotically flat spacetime using a position-space analysis of the Weyl tensor. Starting from the Iyer-Damour multipole solution in harmonic gauge, we obtain an infinite tower of antipodal matching relations across spatial infinity for all five Newman-Penrose Weyl scalars, at linear order in $G$ and for the leading matter-induced logarithms at order $G^2$. We connect the relation relevant to the logarithmic soft theorem to the radiative-gauge formulation of Boschetti-Campiglia and Compère-Robert. We then compute the required asymptotic fields directly from scattering data, including matter contributions and nonlinear effects responsible for graviton drag. Combining these results with the Newman-Penrose evolution equations yields position-space proofs of the classical leading and logarithmic soft graviton theorems, independently confirming the frequency-space derivation of the latter originally performed by Laddha and Sen.

We study nonlinear scalarization of Schwarzschild black-holes for a phantom scalar coupled to the Gauss–Bonnet invariant. Three polynomial couplings satisfying $\zeta''(0)=0$ are introduced to investigate its nonlinear coupling dependence. Since the phantom factor $\epsilon$ disappears in the probe scalar equation, its nonlinear evolution is the same as in the canonical scalar theory. We construct nodeless probe solutions and fully backreacted two branches of lower and primary. At equal mass and equal temperature, respectively, the lower branches have higher Wald entropy and lower Helmholtz free energy than primary branch, but their heat capacities are negative. This implies that lower branch favors than primary branch. Finally, we show that there is no nonlinerly stable scalar phase for a phantom kinetic theory.

Primordial magnetic fields (PMFs) are anticipated to be a cosmological candidate for generating a stochastic gravitational wave background (SGWB) through their anisotropic stress. In particular, if parity violation is present in the production of PMFs, it can induce a helical component in the PMFs, leading to circular polarization in the isotropic SGWB. In this study, we phenomenologically consider parity-violating inflationary magnetogenesis and compute the intensity and circular polarization of the SGWB for several assumed power spectra of helical PMFs. Using the planned sensitivity of the LISA-TAIJI network, we calculate the signal-to-noise ratio (SNR) and perform a Fisher forecast to assess the feasibility of constraining the parameters of helical PMFs. We conclude that it is possible to estimate the helical-to-non-helical power ratio~$r_H$ with $\mathrm{SNR}^{V}>2$ if the PMF strength is $\mathcal{B} \gtrsim 10~\mathrm{nG}$ ($50~\mathrm{nG}$) in the case of the delta-function-type (scale-invariant-type) PMF spectrum. Our results offer a useful criterion that indicates the future observational limit on helical PMFs at the small scale $k_\mathrm{LISA} \approx 10^{12}~\mathrm{Mpc}^{-1}$.

We investigate whether a spherically symmetric black hole can have a complete inner end at finite, nonzero areal radius while satisfying the standard energy conditions sufficiently far outside its horizon. Retaining two independent metric functions, we treat both null-type and spacelike-type asymptotic throats and derive a necessary and sufficient integral criterion for causal geodesic completeness. Under boundedness and finite-limit assumptions on the independent curvature components, null-type ends have limiting curvature fixed by the throat radius, whereas spacelike-type ends admit an additional nonnegative curvature parameter. We obtain criteria for bounded curvature in timelike and null parallel-propagated frames. Complete spacelike-type examples can have bounded scalar invariants and bounded timelike-frame curvature but unbounded null-frame curvature at infinite affine parameter. We also prove that the radial null energy condition must fail arbitrarily close to every complete inner end in the stated class. Nevertheless, explicit real-analytic constructions with either type of throat satisfy the null, weak, dominant, and strong energy conditions throughout a sufficiently distant exterior region. Smooth constructions can become exactly Schwarzschild beyond a finite radius. These results establish the compatibility of complete asymptotic throats with exterior energy conditions while distinguishing completeness from different levels of curvature regularity.

We study wave-optical imaging of two nearby, mutually incoherent point sources by a Schwarzschild black hole. Using the spherical-harmonic addition theorem, we construct partial-wave fields for arbitrary source directions and form images through a finite-aperture Fourier transform. To isolate the binary structure, we compare the binary image with that of a single source of equal total brightness placed at the brightness centroid. Expanding about the centroid removes the first-order term exactly, so the leading structural correction is controlled by the second central moment, $\mu_2=4a^2q/(1+q)^2$. Numerical calculations confirm the expected dependence of the residual on source half-separation and brightness ratio. We then study its wavelength dependence. At long wavelengths, the imaging kernel varies little across the source separation, making the binary nearly indistinguishable from the centroid reference. As the wavelength decreases, finer fringes enhance the residual, which grows by about a factor of three over $3\leq M\omega\leq12$ ($2.09\geq\lambda/M\geq0.52$), even though the pair remains unresolved in the Rayleigh sense. Meanwhile, the second-order approximation gradually breaks down: its relative error first reaches unity for $17<M\omega<18$ ($0.349<\lambda/M<0.370$), indicating the need for higher-order source moments. These results demonstrate that the distinguishability of a nearby binary is intrinsically chromatic and identify the wavelength range in which the binary is both detectable through its residual and accurately described at second order.

We investigate primordial tensor perturbations in a Lorentz violating inflationary framework with non-canonical scalar field dynamics. Using an Einstein-Æther type with a higher order kinetic term $K_3X^2$, we derive the tensor propagation speed and its dependence on an effective Lorentz violating coupling. We consider an analytically tractable potential free background and study two representative couplings, $q_k=\lambda_T\phi_k^2$ and $q_k=\lambda_T\phi_k^4$. The resulting tensor spectral index $n_T$ and its running $\alpha_T$ satisfy distinct consistency relations, providing potential signatures of Lorentz violation in the primordial gravitational wave spectrum. We derive corresponding constraints from the tensor tilt and running and compare them with the stringent late-time bound on the gravitational wave speed from GW170817/GRB170817A. We emphasize that translating this bound into primordial constraint requires an assumption about the evolution of tensor sector coupling between inflation and the late Universe. Our results demonstrate that primordial tensor observables can provide a complementary probe of Lorentz violation and its interplay with non-canonical inflationary dynamics.

We study the complex saddle structure of singly rotating Kerr–AdS$_5$ black holes using a two-variable reduced model in the grand canonical ensemble at fixed angular velocity, $\Omega$. The small and large black hole saddles merge at a critical point where one Takagi singular value of the complex Hessian vanishes, identifying the soft mode associated with the merger. This merger remains distinct from the Hawking–Page transition throughout the physical domain $|\Omega| < 1$. For the reduced integral with the standard measure, we show that thermal AdS dominates uniformly in a complex neighborhood of each real merger point when Newton's constant $G$ is sufficiently small. Consequently, this neighborhood contains no zeros of the partition function, even though the local saddle merger is described by Airy-type behavior. The Fisher zeros instead accumulate near the Hawking–Page coexistence line, with spacing of order $G$, through interference between thermal AdS and the large black hole saddle. We also show that the real quasi-Euclidean Kerr–AdS$_5$ family satisfies a strict asymptotic Kontsevich–Segal–Witten (KSW) phase bound for $|\Omega| < 1$, with the merger point lying inside the allowed domain. In the fixed angular momentum extended ensemble, two such merger points combine into a cusp with a contour-dependent Pearcey approximation. These results distinguish local saddle degeneracies from global phase coexistence and clarify the different roles of Takagi modes, phase transitions, and zeros of the partition function in the complex black hole saddle structure.

The extreme environment within neutron stars presents the opportunity to probe the nuclear equation of state at high densities while studying the properties of these stellar remnants. Historically, the equation of state and neutron star mass distribution have been inferred separately, with the latter often simply assumed to be fixed in studies of the former, but the dependence of the equation of state on neutron star mass indicates they should be inferred together. In this work, we extend the generalized version of the popular RIFT algorithm known as Hyperpipe to interface with flexible, user-provided priors that will facilitate joint inference of equation of state and binary neutron star population hyperparameters. We demonstrate this framework's utility via application to a combination of several existing observations, particularly including massive galactic pulsars, double neutron star systems, millisecond X-ray pulsars, the gravitational wave event GW170817 and the nuclear symmetry energy, within the context of a widely-adopted parametric EOS family and a simple Gaussian population model. We recover parameters consistent with previous analyses of the EOS and binary neutron star population, finding the latter to fit a bivariate normal distribution with mean $(\mu_1,\mu_2) = (1.39,1.27) M_{\odot}$ and width $\sigma = 0.08 M_{\odot}$. Furthermore, we implement novel coordinate transformations in our pipeline, with which we have discovered that the ad hoc prior boundaries used for this EOS family may be too restrictive. We present results with relaxed yet still physical prior boundaries, noting vastly improved hyperparameter posteriors and modestly different equation of state inferences.

Recent DESI observations hint at a preference for dynamical dark energy with an equation of state (EoS) that crosses the phantom divide at $w=-1$. In this work, we investigate metastable dark energy (DE) on the minimal phantom brane. Braneworld effects lead to $w < -1$ at early times, whereas metastable decay of DE results in $w > -1$ at late times. We consider three metastable decay prescriptions on the phantom brane: an exponentially decaying DE component (M1), decay of DE into non-baryonic dark matter (M2), and decay into dark radiation (M3). Using CMB observations, DESI DR2 BAO measurements, and the DES-Dovekie Type Ia supernova sample, we compare these models with $\Lambda$CDM, the Chevallier–Polarski–Linder (CPL) parametrization, and the minimal phantom-brane model with a non-decaying $\Lambda$. We find that metastable models on the brane are preferred over $\Lambda$CDM, their decay rates being $\Gamma/H_0=0.362\pm0.086$, $0.539\pm0.125$, and $0.483\pm0.112$ for M1, M2, and M3, respectively. Best fits of metastable models improve over $\Lambda$CDM by $\Delta\chi^2_{\rm MAP}=-17.14$, $-18.76$, and $-18.22$, while the corresponding $\Delta{\rm DIC}$ values are $-8.66$, $-9.63$, and $-6.56$. Braneworld screening drives effective phantom behaviour at $z\gtrsim0.4$, while DE decay drives the EoS toward non-phantom values closer to the present epoch, with the phantom divide $w=-1$ being crossed at $z \simeq 0.3$–$0.4$. These results show that the interplay between metastable decay and phantom-brane screening provides a simple physical mechanism for an effective crossing of the phantom divide consistent with DESI observations.

We present a consistent treatment of regularization, renormalization, and resummation in a framework involving a contracting phase, a non-singular bounce, and inflation with a sharp transition from slow-roll to ultra-slow-roll, enabling primordial black hole production. Within an effective field theory approach, we compute quantum loop corrections to the power spectrum across all phases. Quadratic UV divergences are removed through renormalization, while logarithmic IR divergences are softened via resummation, demonstrating scheme independence. The inclusion of contraction and bounce allows the generation of solar-mass PBHs, $M_{\rm PBH}\sim{\cal O}(M_\odot)$, with minimal inflation $\Delta N_{\rm Total}\sim{\cal O}(60)$, thereby evading the no-go theorem. For $0.88\le c_s\le1$, the peak spectrum amplitude lies within $10^{-3}\le A\le10^{-2}$, preserving causality and unitarity. PBH abundances across $10^{-33}\!-\!10^{-27}$ and $10^{-6}\!-\!10^{-1}M_\odot$ are confronted with microlensing constraints to control PBH overproduction.

We propose a holographic dual of the relative entropy of entanglement for a boundary tripartition $A:B:C$. Our proposal is that, at the leading order, \begin{align} E_R(\rho_{AB}) = \frac{1}{4G_N}\Big[\mathrm{Area}(\Gamma_{\min}) - \mathrm{Area}(\gamma_{AB})\Big] \notag \end{align} where $\Gamma_{\min}$ is the minimal bulk tripartition surface and $\gamma_{AB}$ is the minimal surface homologous to $AB$. For a general random tensor network, we prove the corresponding upper bound by constructing a separable state associated with $\Gamma_{\min}$ and evaluating its relative entropy. We also establish the matching lower bound rigorously for networks of one, two, and three Haar random tensors by bounding the maximal tripartite product-state overlap. In appropriate geometries, the minimal tripartition surface can form a nontrivial tri-junction resembling the Mercedes logo. The proof proceeds by sequential optimization over candidate product states, which has a natural geometric interpretation as a local search for the minimal tripartition surface.

We revisit the Reissner-Nordström (RN) geometry within the coherent quantum black hole framework, introducing a version that remains well-behaved at short distances while preserving the expected classical behavior at large scales. The key ingredient is a smooth Gaussian regularization, which replaces the usual sharp cutoff and {suppresses} the unphysical oscillations. This construction introduces a characteristic core radius $R_{\rm s}$, constrained relative to the mass $M$ and charge $Q$ to ensure either a {Ricci-regular} center or a softened integrable singularity. Near the origin, the spacetime exhibits distinct behaviors depending on the choice of parameters. When $R_{\rm s}$ satisfies the critical relation $R_{\rm s}^* = \sqrt{\pi}\,R_{\rm Q}^2 / R_{\rm M}$, the geometry is {Ricci-regulFar}, while deviations from this value produce a milder, integrable singularity. {We clarify that for generic parameters, the Kretschmann scalar retains a $1/r$ divergence even at $R_{\rm s}^*$, so the center is not fully regular in the sense of finite curvature invariants.} The effective stress-energy tensor can be interpreted as an anisotropic fluid, whose density and pressure smoothly interpolate between the quantum-dominated core and the classical RN region at large radii. The Misner-Sharp mass accumulates gradually from the center, recovering the ADM mass asymptotically. The quantum scale also modifies the horizon structure, giving rise to standard, extremal, or horizonless configurations depending on the ratios $\alpha=R_{\rm Q}/R_{\rm M}$ and $\beta=R_{\rm s}/R_{\rm M}$. Photon motion is correspondingly affected: the photon sphere moves inward, light deflection and Shapiro delay are slightly reduced, and the resulting shadow appears more compact and smoother, reflecting the quantum-corrected geometry.

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 $C_{\rm can}^{\rm EH}=(9aQ^2/10)\left(\begin{smallmatrix}0&-Q\\-Q&M\end{smallmatrix}\right)$, 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 $\frac{Q}{M}$ 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.

In this note we present a direct relation between the geometrical definition of a quasi-Einstein metric and Horava gravity: the solutions of the large-distance effective action of Horava gravity that are static and orthogonal are quasi-Einstein metrics. The converse is also true if the function over the quasi-Einstein manifold satisfies a given equation.

This paper develops a weak-field, non-metric operational account of gravitational light deflection. In the isotropic formulation of the Schwarzschild weak field, the non-metricity trace 1-forms W and P are computed explicitly and shown to determine the optical response through the exact relation $d\ln n=W-4P$, $n=g/f$. Thus the effective refractive index governing null propagation is not introduced as an external optical analogy, but is tied directly to the trace sector of non-metricity. To connect the trace geometry with matter, an effective scalar calibration potential $\chi$ is sourced by an observer-projected macroscopic dilation current, yielding $\nabla^2\chi=-\kappa\rho$ in the static weak-field limit. The point-mass calibration fixes $\Phi=\chi/C_0\simeq 2GM/(rc^2)$, and the resulting optical calculation gives the Eddington deflection angle $4GM/(bc^2)$. The significance of the result is not a modified numerical prediction, but a closed weak-field chain from macroscopic dilation sourcing to non-metricity traces, effective refractive index, and light deflection, without postulating a microscopic deformation law for material rods or clocks.

We present a systematic analysis of spherically symmetric accretion flows onto thirteen non-rotating black hole spacetimes, including charged and regular black holes, scalar and dilaton fields, dark energy, cosmological constants, modified gravity, and parametrized metrics. We generalize the Michel solution to arbitrary diagonal spacetimes and investigate the density, temperature, velocity, Mach number, mass accretion rate, and bremsstrahlung luminosity equilibrium profiles. Using the Schwarzschild solution as a reference, we find significant deviations in the accretion flow, with cosmological-constant and dark-energy models strongly suppressing accretion, while regular and Yukawa-like spacetimes generally enhance it. We provide fitting formulas for the accretion rates and luminosities as functions of the spacetime parameters. We then explore two astrophysical applications: accretion onto supermassive black holes, such as Sgr A* and M87*, and the inferred progenitor masses of the intermediate-mass black holes associated with the GW190521 gravitational wave event. We find that observational uncertainties may allow us to probe signatures of deviations from the Schwarzschild spacetime.

In a low-energy effective field theory (EFT), scaling logarithmic terms arise from the renormalization of higher-dimensional couplings that absorb divergences generated by loop integrals with lower-order vertices. Consequently, leading logarithms (LLs) are generated entirely by the leading-order Lagrangian, rendering them universal low-energy predictions. Adapting techniques developed for chiral perturbation theory, we analyze the series of LLs in the EFT of general relativity. As a concrete application, we compute LL corrections to the scalar pole mass up to three-loop order and demonstrate that they can be determined recursively to arbitrary loop order. To confirm the physical validity of our results, we carry out the calculation using a general gauge-fixing parameter and explicitly verify its complete cancellation in the physical observable.

The massive Klein-Gordon equation on the Schwarzschild exterior reduces to a radial differential equation of confluent-Heun type. We present its exact reduction by rigorously retaining a subleading centrifugal term that preserves the horizon indicial exponents but critically shifts the accessory parameters. Within the Svartholm–Schmidt hypergeometric-expansion framework, we derive the three-term recurrence relation and establish the corrected continued-fraction compatibility condition matching the minimal tail to the lower-end recurrence. Crucially, we demonstrate that the physical compactification coordinate $z=(r-1)/r$ shifts the irregular singular point to $z=1$, inherently transforming the hypergeometric expansion into a five-term recurrence that cannot degenerate to three terms. To circumvent this obstruction, we construct the horizon-normalized physical branch via a direct Frobenius series at $z=0$. This representation exhibits high-order convergence and near-precision-floor residuals against the exact radial ODE, while clarifying why quasinormal-mode spectral selection remains a connection problem at the irregular singular endpoint.

Recent cosmological results, including the persistent $H_0$ tension and indications of dynamical dark energy, have raised the possibility that the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model may be incomplete. At the same time, theoretical developments based on swampland conjectures indicate that the realization of a stable de Sitter vacuum within string theory is challenging. Motivated by these observational and theoretical considerations, we investigate an interacting $\Lambda$ scenario characterized by a general linear coupling in the dark sector. At the background level, this model naturally allows the dark energy density to evolve from negative to positive values, opening the possibility of a transition from an anti-de Sitter-like phase to the de Sitter-like phase inferred by current observations. We derive the analytic background solutions and perturbation equations, discuss the physically acceptable region of parameter space, and constrain the model with DES-Dovekie type Ia supernovae, DESI BAO and CMB data. Our analysis suggests a parameter space allowing the dark energy density to change sign while maintaining positive dark matter density, motivating further investigation of an interaction-driven anti-de Sitter to de Sitter transition.

We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the IMRPhenomD waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs – larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as IMRPhenomHM. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, SymDALI) which computes derivatives symbolically via Wolfram Language.

Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks to satisfy the underlying physical laws. The resulting continuous representation does not require a predefined computational mesh and can be evaluated at arbitrary points within the training domain. In this work, we investigate the application of PINNs to Einstein's equations of General Relativity. We discuss the mathematical formulation, network architectures, loss functions, and training strategies used to obtain accurate spacetime solutions, and demonstrate the approach through a series of standard benchmarks from Numerical Relativity. We then extend the method to a more astrophysical setting by considering the dynamical evolution of an isolated solitonic boson star. Our simulations show that a PINN operating directly in three-dimensional Cartesian coordinates can reproduce the equilibrium structure of a highly compact boson star and recover its characteristic radial oscillation frequencies. These results establish PINNs as a viable complementary framework for solving coupled matter-Einstein equations and exploring alternative formulations in numerical relativity.

Energy transport across conformal interfaces is universal in two spacetime dimensions, but its higher-dimensional counterpart has remained largely unexplored. In higher dimensions, scattering can depend on additional kinematic data, such as the angle of incidence, and conformal symmetry is far less restrictive. We use gravitational holography to study this problem. For a broad class of AdS$_d$-sliced domain-wall geometries, we derive a closed-form expression for the energy transmission coefficient in terms of the bulk warp factor. Our formula reproduces known two-dimensional holographic results and extends them to arbitrary dimension. Within this class, we establish different aspects of higher-dimensional universality. In particular, we show that the transmission is independent of the incidence angle and of the profile of the incident perturbation. We also derive bounds on transmission controlled by central-charge-like quantities characterizing the number of degrees of freedom of the theories on the two sides of the interface. This provides the first explicit result for reflection and transmission across conformal interfaces in higher dimensions, where no CFT-based results are currently available.

We consider general EMD-like theories involving arbitrary numbers of both Maxwell fields and dilatonic scalars. We study charged black holes and derive several algebraic and differential relations among the thermodynamic quantities, scalar charges and the non-extremal parameter. These allow us to obtain two sets of master equations of thermodynamic quantities, depending on the choice of basic variables parameterizing the system. Solutions to either set of the master equations give rise to all the thermodynamic quantities, without constructing black hole solutions. We obtain all the thermodynamic quantities perturbatively in the power series expansions of charges, which we then verify using perturbative black hole solutions up to and including the quartic order in charges.

DESI Data Release 2 has heightened interest in cosmologically coupled black holes (CCBHs) as an explanation for accelerating late-time expansion, but known models for CCBHs grow too slowly to drive it. We construct at linear order a solution to General Relativity whose Hernandez-Misner-Sharp mass passively grows $\propto a^\kappa$ as the universe expands. The constant $\kappa$ enters all eigenvalues of the Weyl and stress-tensor operators, so growth is unambiguously physical in both free-field and material sectors. The solution is causal over spacetime relevant for stellar collapse compact objects. A cloud of energized vacuum emerges at $\kappa = 3$, complementing the $a^3$ scaling predicted elsewhere for the masses of energized vacuum black holes. This first step toward $\kappa \sim 3$ CCBH exact solutions enables observational tests with pulsar binaries.

Claims concerning a dynamical equivalence between general relativity and two reformulations of it, in which gravity is encoded in torsion and non-metricity respectively, have attracted some attention. If taken to be true, this 'Geometric Trinity' suggests that it is impossible to determine, even in principle, whether one inhabits a spacetime solution possessing curvature, torsion or non-metricity (insofar as the probes of geometry are paths of test particles). This claim is in direct tension with the long tradition of studying gravity as a gauge theory, in which distinct geometric attributes couple to distinct properties of matter (such as energy-momentum to curvature and spin angular momentum to torsion). In this short paper, I compare these two conflicting frameworks for geometrizing spacetime and describe the precise source, nature and implications of their disagreement. The equivalence claim holds only under a substantive restriction on the matter sector, namely that matter does not couple to an independent affine connection. Because the relevant couplings remain beyond current empirical reach, the choice between the frameworks turns on a trade-off among ontological, epistemic, and methodological forms of parsimony.

In 2023, pulsar timing array (PTA) collaborations around the world announced evidence for a nanohertz gravitational-wave background (GWB). Beyond increasing the detection significance, the next major goal is to characterize the GWB and identify its source(s). The typical model-comparison metric used in PTA analyses is the Bayes factor (BF). However, BF computation methods used in the PTA literature, such as product-space sampling and thermodynamic integration, are computationally expensive or inefficient if the models compared are dissimilar or non-nested. In this work, we introduce a PTA model-comparison method using a combination of normalizing flows, nested sampling, and a PTA likelihood that is marginalized over all non-GWB parameters. The flows are trained using a newly-developed Python package coppuccino, which learns the data's copula: the dependence structure after transforming to uniform marginals. We validate the method on both analytic targets and simulated PTA data, recovering the analytic evidence within error bars and achieving an area-under-the-curve (AUC) score of 0.996 when treating the BFs as binary classifiers of the injected models. The result is a method to perform Bayesian model comparison of arbitrary GWB spectral models in minutes on consumer hardware.

In this article, we analyze plane-symmetric solutions to the relativistic Euler equations on spatially flat spacetimes with decelerated expansion. We consider a linear equation of state $p(\rho)=K\rho$ and power law inflation $a(t)=t^{\alpha}$, where $0<K<\frac{1}{3}$ and $0\leq\alpha<1$. Previous results imply nonlinear stability of the homogeneous and isotropic solution above an expansion threshold $\alpha_\text{crit}=\frac{2}{3(1-K)}$. We prove that at and below this critical expansion rate there exist arbitrarily small data that exhibit finite-time singularity formation of the shock type, i.e., gradient blowup while the solution stays bounded. For this type of data, we establish lifespan estimates that are polynomial below and exponential at the critical threshold. In addition, we prove a theorem based on energy estimates that provides lower bounds on the lifespan of plane-symmetric solutions generated from small initial data and generalizes to solutions without symmetry in $3+1$-dimensions.

Gravitational-wave (GW) “dark siren” techniques, namely the statistical association of GW events with a galaxy catalog, have so far been used as a cosmological tool. Yet this association carries distinctive astrophysical information that remains unused—specifically, how compact binaries populate galaxies and the identities of individual hosts. In this work, we turn the dark-siren program into an astrophysical probe by inferring both simultaneously within a single hierarchical framework. The method reduces the many potential hosts to a compact, probabilistically ranked target list, providing a direct follow-up decision tool. Applied blindly to GW170817, it recovers NGC~4993 as the highest-ranked host and constrains the galaxy luminosity weighting, mildly favoring non-uniform host weights. Fixing the galaxy weighting can instead degrade host identification and even favor the wrong host. This framework recasts dark sirens as a potentially unique probe of the astrophysics of electromagnetically dark compact-binary mergers.