External matter distributions can substantially reshape the strong field environment of compact objects, yet this effect is usually neglected in idealized isolated models. In this work, we investigate geometrically thin, optically thick relativistic accretion onto a static axisymmetric space-time that describes a slightly deformed compact object immersed in an external quadrupolar field as an exact solution of vacuum Einstein field equations. Our aim is to determine whether such locally geometries can produce distinctive accretion signatures and, more broadly, to identify the physically meaningful radial domain over which the local solution remains self-consistent. We show that the external quadrupolar distortion leaves a clear imprint on both orbital dynamics and accretion structure. We further find that the outer edge of the radiating region is closely tied to the transition between radiation pressure and gas pressure dominance, which may link the geometry to the thermodynamic properties of the flow. Therefore, the local nature of the distorted spacetime is not merely a formal geometric feature, but has observable consequences for the morphology and emission properties of accretion flows.

General relativity has achieved remarkable experimental and observational success. Critically, recent data from the LIGO-Virgo-KAGRA, Event Horizon Telescope, and GRAVITY collaborations are often credited with \textit{demonstrating} the existence of black holes, but in fact they only provide evidence for objects that should be regarded as black hole candidates. While current data are in striking agreement with the predictions for Kerr black holes, they can only rule out specific alternative models of compact objects rather than provide conclusive proof of black holes. More fundamentally, and independent of whether or not black holes exist, general relativity itself imposes limits on what can be observationally established. Essentially, no observational data is sufficient to confirm the existence of black holes.

In this work, we derive an exact black hole solution in higher-order curvature gravity by coupling an electromagnetic sector formulated within the ModMax framework to a quintessence dark energy component. Focusing on purely electrically charged configurations, we analyze the thermodynamic and geothermodynamic properties of the solution to investigate its stability and phase structure. Within this sector, the ModMax theory effectively reduces Maxwell electrodynamics up to a rescaling of the electric charge, and thus the obtained solution corresponds to a consistent subset of the broader nonlinear theory. Using thermodynamic geometry, we examine microscopic interactions and phase transitions, showing that divergences in the thermodynamic curvature coincide with the vanishing of the heat capacity, confirming the consistency of the phase structure. We further explore the optical properties of the black hole by studying null geodesics and determining the photon sphere and the corresponding shadow radius for different values of the quintessence state parameter $\omega$. Exact analytical expressions for the photon-sphere radius are derived, revealing that higher-order curvature corrections and quintessence significantly enhance the shadow size, whereas the electric charge has the opposite effect. Notably, quintessence is found to have a more pronounced impact on the shadow than the charge. These results highlight that dark energy and higher-order curvature corrections can yield potentially observable signatures in black hole shadows.

Generalized vector-tensor theories of gravity have drawn attention for admitting hairy black hole solutions, thereby circumventing the standard no-hair theorems. It remains an open question, however, how such black holes may form starting from reasonable initial conditions. It has been suggested that vector hair may grow spontaneously as a result of the field developing a negative effective mass squared $-$ the so-called spontaneous vectorization mechanism. We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationary and axisymmetric solutions of interest in general relativity. More precisely, we prove that the appearance of a negative effective mass squared for the vector field must necessarily be accompanied by ghost- or gradient-type instabilities. Demanding the absence of such instabilities translates into interesting bounds on the coupling constants of the theory as functions of the black hole parameters. In particular, we discover that a Kerr black hole may become unstable when the spin increases above a certain critical value.

The Eisenhart-Duval lift (ED) geometrizes classical dynamics by embedding their trajectories into null geodesics of a higher-dimensional Lorentzian spacetime. However, such a construction requires a natural Hamiltonian, that is, quadratic in the canonical momenta. As a consequence, mini-superspace cosmological models governed by non-natural Hamiltonians cannot admit an ED lift. Effective models in Loop Quantum Cosmology provide a concrete example: polymer-modified Hamiltonians become non-polynomial in the momenta and therefore fall outside the metric framework of the ED lift. We thus establish a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions. Quantum-corrected bounce models therefore illustrate a structural limitation of metric geometrization within the ED framework.

We construct a new Ricci-flat metric by demagnetizing the recently reported Kerr-Bertotti-Robinson (KBR) solution. The metric is a deformation of the Kerr metric characterized by a parameter $B$, so that the asymptotic Kerr becomes a regular dome of spindle shape with north and south poles. Despite lacking an asymptotically-flat region, we find that the first law of black hole thermodynamics can be established. Some thermodynamic relations are identical to those of the Kerr black hole, as if the constant $B$ is absent. Our Ricci-flat rotating metric serves a neutral seed for a variety of inequivalent schemes of magnetizing the Schwarzschild and Kerr black holes.

We construct charged black hole solutions in bumblebee gravity coupled to a general class of nonlinear electrodynamics (NLED) using an auxiliary Maxwell-scalar formalism. The norm-fixed radial configuration of the bumblebee vector makes the solutions asymptotic to a conical Lorentz-violating vacuum and requires stringent nonminimal bumblebee-NLED couplings. The general black hole solutions contain independent mass and charge parameters. There are two sources of singular behavior at the center: one is due to the Schwarzschild-type pole and the other is the residual conical singularity of the Lorentz-violating vacuum. By fine-tuning the mass-charge relation, one can generally remove the pole singularity, giving rise to marginally regular black holes. For a suitable NLED theory such as Born-Infeld theory, both singularity sources can be removed at the cost of requiring both the mass and the charge to be fine-tuned to specific functions of the coupling constants. The resulting solutions describe regular horizonless spacetimes interpolating from AdS or dS cores to Lorentz-violating vacua.

We construct new families of everywhere regular, asymptotically flat solitons in the Einstein--Proca model, obtained as self-gravitating continuations of flat-spacetime (singular) Proca multipoles. First we consider static and axially symmetric solutions, organized by a multipole number $\ell$. Two distinct classes arise: electric-type configurations, which include the spherical Proca stars as the $\ell=0$ case, and magnetic-type configurations, which have no spherical counterpart and start at $\ell=1$. Then we construct hybrid solutions as nonlinear superpositions of electric and magnetic multipoles. These have non-vanishing local angular momentum density but vanishing total angular momentum, and in some cases have no north-south $\mathbb{Z}_2$-symmetry. By performing dynamical evolutions of Proca stars in the new magnetic and hybrid sectors, we show they are unstable, decaying to the (static) prolate Proca stars or the (stationary) spinning Proca stars, previously identified as dynamically robust, electric sector configurations. In some cases, they can also collapse into a black hole.

Traversable topological bridges traditionally require exotic matter, violating the Null Energy Condition (NEC). This essay investigates whether matter-vacuum coupling can circumvent this necessity. Focusing on zero-tidal-force solutions, we establish a rigorous no-go theorem for static configurations, proving that such coupling cannot bypass the requirement for NEC violation. We demonstrate that the geometric flare-out condition is incompatible with NEC-compliant sources, regardless of the coupling $Q$ or equation of state. Crucially, the vacuum fails to shield the throat; instead, interaction gradients mathematically obstruct the required geometry. This result suggests that causality protection is inherent in the field equations, rendering the vacuum's evolution a regulator rather than a facilitator of topological shortcuts, thereby reinforcing the robustness of classical energy conditions.

Graviton lasers have been considered in the past, \cite{gl}, but practical terrestrial implementations appear infeasible. The absence of any known mechanism to reflect gravitons means that it remains unclear how a graviton beam could be directed repeatedly through a putative lasing medium. Astrophysical graviton lasing is still a possibilty as circular graviton orbits around blackholes afford the possibility of an arbitrarily long path length through the lasing medium of ultra-light dark matter \cite{bhgl,nhaxs}. In this essay, we consider the possibility of a graviton laser that could be constructed in a laboratory setting. The graviton lasing medium could be one of many possible gravitating systems, of which we give three possible examples. We calculate the possibility of reflecting the gravitons by using the conversion of gravitons into photons in an external magnetic field, the Gertsenshtein effect, \cite{Gertsenshtein1962}. We may convert the gravitons to photons, then reflect the photons, then reconvert the photons into gravitons via the same effect, and then pass them through the graviton lasing medium. With an identical apparatus on the other side, we can essentially extend the path length of the gravitons through the lasing medium as arbitrarily long as desired.

The quasi-normal modes of black holes play various important roles in gravitational wave theory, signal modeling, and data analysis; however, there remain open questions about their mathematical properties. Aspects of classical polynomial theory have been proposed as a framework to investigate quasinormal mode orthogonality and completeness. We have recently presented a class of polynomials that are "natural" to quasi-normal modes in that they are restricted by the quasi-normal mode boundary conditions, and exactly tridiagonalize Teukolsky's radial equation. In turn, these polynomials may be useful for better understanding the vector space properties of quasi-normal mode solutions to that equation. Here, we provide an overview of these polynomials' analytic properties: their 3-term recurrence relation, ladder operators and governing differential equation. We demonstrate that the natural polynomials for Schwarzschild and Kerr black holes are Pollaczek-Jacobi polynomials with complex valued parameters. Along the way, we observe a novel property that is particular to Schwarzschild: the polynomials' 3-term recurrence relation always peaks at the physical overtone index. This work supports the broader application of these polynomials, as well as their extension to black hole spacetimes beyond Schwarzschild and Kerr.

We investigate the superhorizon behavior of scalar hair sourced by black holes in de Sitter spacetime in the linearly coupled shift-symmetric scalar-Gauss-Bonnet theory. Working in the test-field regime, we show that this hair exhibits both temporal and spatial growth on superhorizon scales. This growth is not a special consequence of the black hole, but instead follows from the dynamics of a minimally coupled massless scalar field in expanding de Sitter spacetime. Moreover, it is not even specific to black holes, but also arises for a point scalar charge in de Sitter, indicating that a scalarized black hole acts effectively as a localized subhorizon source of scalar perturbations. Backreaction, when important, first arises on subhorizon scales and does not by itself eliminate the superhorizon profile. The time-dependent scalar hair also carries a steady outward energy flux, which frames the test-field regime as a transient, and helps explain the difficulties encountered in attempts to construct self-consistent static solutions.

This work investigates the mechanism of gravitational baryogenesis (GB) under the formalism of f(R, G_{{\mu}{\nu}}T^{{\mu}{\nu}}) gravity, where R denotes the Ricci scalar, G_{{\mu}{\nu}} is the Einstein tensor and T^{{\mu}{\nu}} represents the energy--momentum tensor. f(R, G_{{\mu}{\nu}}T^{{\mu}{\nu}}) model is considered to evaluate the baryon-to-entropy ratio (BnER), which is subsequently compared against the observational limits. The results obtained exhibit compatibility with the estimated matter imbalance. Moreover, the analysis is extended to generalized GB case, resulting in outcomes that closely match empirical bounds. The findings reveal that the f(R, G_{{\mu}{\nu}}T^{{\mu}{\nu}}) formulation yields a viable theoretical setting for explaining the detected matter-antimatter disparity of the universe, highlighting its relevance in early cosmic evolution. To further validate the models, a chi-square ({\chi}^2) analysis of the Hubble parameter, H(z), and distance modulus, {\mu}(z), is performed, confirming their consistency with current cosmological observations. A comparative assessment simultaneously with the {\Lambda}CDM paradigm demonstrates a satisfactory level of agreement between the proposed model and cosmological observations from CC and Pantheon+SH0ES datasets.

It has recently been revealed that dyonic black-hole spacetimes of a quasitopological non-linear electrodynamic field theory may be characterized by discrete radial regions with the property $dg_{tt}(r)/dr=0$ in which spherically symmetric massive {\it test} shells (Dyson shells with negligible self-gravity) can be supported in static equilibrium states. In the present paper we prove that the dyonic spacetimes of the non-linear electrodynamic field theory may also be characterized by the presence of radial regions with the dimensionless property $d[r\cdot g_{tt}(r)]/dr\to0^+$ in which massive {\it self-gravitating} thin shells that are on the verge of becoming black holes can be supported in static equilibrium states. Intriguingly, it is proved that the discrete radii of these self-gravitating nearly-black Dyson shells are universal in the sense that they are independent of the masses of the central supporting dyonic compact objects.

Motivated by recent work on consistent fluid couplings in $f(R, T)$ gravity, we study cosmology in the nontrivial model $f(R, T) = R + \sigma R T$ using the Brown variational principle for a barotropic perfect fluid. For a flat FLRW universe, we cast the field equations into Einstein-like form and obtain explicit expressions for the effective energy density, pressure and equation of state (EOS) parameter. This allows us to rewrite the null, weak, strong and dominant energy conditions as simple polynomial inequalities. We show that radiation reproduces standard relativistic cosmology, whereas for dust and $\sigma>0$ the effective fluid acquires negative pressure and can drive accelerated expansion. In this dust case, there exists a finite window in the Hubble parameter during which the strong energy condition is violated, but the null, weak, and dominant energy conditions remain satisfied. Conversely, whenever the strong energy condition is imposed, the other conditions are automatically fulfilled. The additional viability requirement $1 + \sigma T > 0$ further restricts the allowed Hubble range and yields an upper bound on $\sigma$ that still leaves a non-empty accelerating regime. Our analysis provides a transparent energy-condition study of a consistent $R\, T$ coupling in $f(R, T)$ cosmology, based on qualitative techniques.

We investigate the quasinormal modes of massless scalar and electromagnetic perturbations in charged Euler--Heisenberg black holes surrounded by perfect fluid dark matter. The quasinormal frequencies are calculated using the asymptotic iteration method and the sixth-order WKB approximation, and the relative deviation between the two methods is quantitatively analyzed to verify the reliability of results. The greybody factors for both perturbations are also evaluated within the sixth-order WKB framework. We systematically examine the effects of the black hole charge $Q$, nonlinear electrodynamic parameter $a$, dark matter parameter $\lambda$, and angular quantum number $l$ on the quasinormal frequencies and greybody factors. We find that these parameters significantly modify the structure of the effective potential barriers, and thus affect the oscillation frequencies, damping rates, and wave transmission and reflection properties of the perturbed fields.

We investigate the consistency in the thermodynamics and the approaches at the equation and action levels for the quantum-improved charged black holes with scale-dependent couplings. For the quantum-improved Reissner-Nordström black holes, we find that the thermodynamic consistency allows both the Newton and electromagnetic couplings to have arbitrary dependence on the radial coordinate. We point out a subtlety in the chemical potential with the scale-dependent electromagnetic coupling in the study of thermodynamics. We also examine the compatibility of the Einstein equations at the equation and action levels with the Bianchi identity, identifying the need for an additional quantum energy-momentum tensor. We then find that the consistency between the approaches at the equation and action levels requires that the Newton coupling satisfy certain property. Finally, we extend the analysis to cosmological solutions, suggesting that quantum-induced modifications can drive the isotropization of the early universe.

In this work, we investigate the cosmological dynamics of a spatially flat Friedmann--Lemaître--Robertson--Walker Universe in the framework of generalized \( \mathcal{F}(\mathcal{R},\Sigma,\mathcal{T}) \) gravity by incorporating gravitationally induced particle creation together with the variable generalized Chaplygin gas scenario. The modified gravitational action depends explicitly on the Ricci scalar \( \mathcal{R} \), the matter-coupling scalar \( \Sigma \), and the trace of the energy--momentum tensor \( \mathcal{T} \), which collectively generate significant corrections to the standard cosmological evolution. The particle creation mechanism is introduced through an open thermodynamic description of the Universe. In addition, the dark sector is modeled using the variable generalized Chaplygin gas formalism. To examine the observational consistency of the model, the free parameters are constrained using the Pantheon\(^+\) Type Ia Supernova compilation together with the combined observational Hubble and Pantheon\(^+\) datasets through a statistical \(\chi^2\)-analysis. The cosmological behavior of the model is further explored through the evolution of the cosmological parameters. Furthermore, the thermodynamic properties of the model are investigated using the apparent horizon formalism. The obtained results demonstrate that the entropy evolution remains physically consistent throughout the cosmic evolution. Hence, the present \( \mathcal{F}(\mathcal{R},\Sigma,\mathcal{T}) \) gravity framework with particle creation provides a viable geometrical description of the late-time accelerated Universe and remains compatible with recent cosmological observations.

Recent cosmological tests have discovered a fresh new set of anomalies in the large-scale isotropy of the universe. Motivated thus by the numerous pieces of evidence for large-scale cosmic isotropy violation with the advent of the 'precision cosmology' era, we are led to explore the viability of anisotropic Thurston geometries, described in William Thurston's geometrization conjecture. In this work, we examine the coherent temperature and polarization signals generated in the CMB sky by such geometries. We begin with introducing Thurston spacetimes as our background model and the formalism we use to obtain the patterns. We then construct a set of transfer equations relative to a given background and solve them for each spacetime geometry. We finally discuss the role of spatial curvature in these FLRW limiting models along with their underlying geometry, and attempt to establish some general results on the symmetries of the patterns produced by their time evolution in terms of the Stokes parameters P, Q, U and V. We show the evolution of temperature and polarization amplitudes in terms of such Stokes parameters at different timestamps and attempt to isolate individual Thurston geometries.

We investigate the imprints on the angular power spectra of cosmological perturbations of a pre-inflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on pre-inflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from LQG. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in pre-inflationary scenarios there is no preferred vacuum state, we adopt the NO-AHD proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a non-oscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard $\Lambda$CDM model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to $\Lambda$CDM for low multipole numbers.

We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying ${\alpha\neq3\beta}$, while the case ${\alpha=3\beta}$ is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.

Hellings-Nordtvedt theory is a vector-tensor theory in which a vector field $A_\mu$ is nonminimally coupled to curvature through two independent interactions $A^2{\cal R}$ and $A^\mu A^\nu{\cal R}_{\mu\nu}$. When supplemented by a potential whose zero-energy minimum occurs at nonzero $A^2$, the restricted $A^\mu A^\nu{\cal R}_{\mu\nu}$ sector is known to admit black-hole and neutron-star solutions with a monopole-like asymptotic vacuum structure. We examine whether this structure is a generic consequence of the nonzero vector vacuum or instead relies on the special Ricci-tensor coupling. By analyzing the field equations near spatial infinity, we show that the asymptotic vacuum condition is incompatible with generic nonzero values of both couplings and instead selects two allowed single-coupling sectors. The $A^\mu A^\nu{\cal R}_{\mu\nu}$ sector reproduces the known monopole-like asymptotics, whereas the $A^2{\cal R}$ sector admits an asymptotically flat Schwarzschild metric with a nontrivial radial vector field. We further compute the Noether mass in the $A^2{\cal R}$ sector, derive the corresponding Solar-System constraints, and construct neutron-star configurations. Although the weak-field deviation is constrained to be small, neutron stars can still show appreciable departures from both general relativity and the Ricci-tensor-coupling sector in their masses, radii, and moments of inertia. Our results identify that the $A^2{\cal R}$ sector of massive Hellings-Nordtvedt theory as a viable and useful framework for studying strong-field compact objects with a nonzero vector vacuum while remaining compatible with weak-field tests.

Continuous gravitational waves, i.e., persistent and nearly-monochromatic signals emitted by asymmetric spinning neutron stars, remain elusive. Searches for these signals from unknown binary systems are the most computationally challenging, but they are essential, given that binary accretion provides a natural mechanism for creating the required asymmetry, and around half of the known pulsars rotating above 25 Hz are part of a binary system. Here we report on a search of a large uncharted parameter-space region: for the first time we cover gravitational-wave frequencies above 520 Hz (from 50 to 1000 Hz), and, for the first time with advanced detectors, orbital periods lower than 3 days are explored. No signal is detected, and we set the most stringent constraints to date on the amplitude of signals of this kind. Our results exclude with $95\%$ confidence neutron stars within 100 pc and rotating faster than $\sim$ 495 Hz from having ellipticities above $5.2 \times 10^{-8}$. Within the same distance our results also exclude r-mode amplitudes above $1.5 \times 10^{-6}$ for stars rotating faster than $\sim$ 740 Hz.

We study the regularized vacuum stress tensor of scalar fields in maximally symmetric spacetime and assess the feasibility of driving primordial inflation or current cosmic acceleration by analyzing the existence of solutions to the Friedmann equation. We find that a conformally coupled scalar field with mass of order $10$ $M_{\text{pl}}$ can be a candidate for both the inflaton and dark energy, suggesting that these two components may have the same quantum origin. In contrast, a minimally coupled scalar field cannot serve as either the inflaton or dark energy regardless of its mass.

Quantum Gravity remains elusive, largely because its observable effects are suppressed by powers of the Planck scale. Direct detection of single gravitons is widely believed to be impossible. Here we propose a concrete astrophysical mechanism that may overcome this suppression. We show that superradiant axion-like-particle clouds surrounding rotating black holes can generate multimode squeezed states of gravitons containing up to $10^6$ - $10^7$ correlated quanta. Such states exhibit distinctive polarization correlations and quantum-noise signatures that could be detectable in future gravitational-wave interferometers. Observation of these signatures would constitute direct evidence for the quantum nature of gravitational radiation. Conversely, their absence can place constraints on axion-cloud lifetimes. Our approach also provides a test of General Relativity as an effective field theory.

Roger Penrose introduced the concept of the trapped surface: a spacelike hypersurface where the two null normals have negative expansion. The trapped surface along with the null convergence condition leads to null geodesic incompleteness. If an event horizon forms, the trapped surface is also always behind it, providing evidence for the weak cosmic censorship conjecture. When the null convergence condition is violated, as in the case of semiclassical gravity, trapped surfaces lose these guarantees. A generalized notion, the sufficiently trapped surface, accommodates weaker energy conditions consistent with quantum fields. This concept restores key roles in singularity and area theorems and continues to support the weak cosmic censorship conjecture.

Motivated by the central role of the Zel'dovich approximation in the description of cosmic structure formation through gravitational collapse, we investigate Burgers-type dynamics in a spherically symmetric gravitational field. In the Newtonian setting, we derive perturbatively the catastrophe time for radial motion by imposing the loss of invertibility of the Lagrangian map. We show that the perturbative expansion is controlled by the dimensionless parameter $ \alpha=\mu/{r_0^3 v_0(r_0)'^2}, $ rather than by the local gravitational acceleration alone. Hence, the expansion remain valid even when gravity is strong. We then extend the analysis to radial geodesic motion in Schwarzschild spacetime.

It has been known that gravitational waves (GWs) transfer energy to viscous matter through which they propagate, but the effect is too weak to be astrophysically significant. Using linearized perturbations about a Minkowski background, we previously showed that the interaction can become important when the distance between matter and source is smaller than the GW wavelength. Here, we review extensions to more realistic backgrounds, namely Schwarzschild spacetime and a static spherically symmetric setting. We find that GW damping and the associated heating of the viscous fluid are enhanced, and can lead to substantial attenuation or even gamma-ray bursts. We investigate astrophysical scenarios where these effects may be relevant, including core-collapse supernovae, binary neutron star mergers, and accretion onto binary black hole mergers.

When considering how self-interaction affects an object's motion, it can be convenient to decompose the self-force into conservative and dissipative pieces. As a toy model for understanding such decompositions of the gravitational self-force, we consider objects that do not affect the spacetime, but are instead coupled to a nonlinear scalar field. There is then a standard splitting of the first-order scalar self-force into conservative and dissipative components. Multiple criteria can be used to obtain this splitting, all of which imply the same result. However, the implications of these criteria generically differ at higher orders. Demanding that any reasonable conservative sector be Hamiltonian, we identify multiple possible definitions of the conservative second-order self-force. Motivations for these possibilities and their properties are discussed and relevant Hamiltonians are obtained. We assume the existence of a three-point function with certain properties that is a generalization of the Detweiler-Whiting two-point function. These results apply to the two-body problem but are restricted to unbound scattering trajectories, due to infrared divergences that arise for bound orbits.

In recent years, there have been increasing challenges to the cosmological principle, based on new observations of e.g. supernovae and the cosmic bulk flow. As a result, the cosmological community is speaking their concern for the cosmological principle, and from which scales onwards it should apply. In this context, there is a desire to understand more fully the properties and signatures of cosmologies not obeying the cosmological principle. In this article, we let go of the demand of cosmic isotropy, and instead assume only spatial homogeneity in our cosmological models. We follow the results of our previous works [see citations in the list of references], and here bring these together into one unified picture, with the goal of describing the signature(s) of anisotropy in anisotropic cosmological models. We first introduce the Bianchi models -- a particular instance of spatially homogeneous cosmologies -- and show that a metric can be constructed for them when an appropriate collection of desired Killing vector fields is supplied. Then, we give the perturbations of the Friedmann equations in such Bianchi models, in the Newtonian gauge, derived using much the same methodology as applicable to the FLRW models. We show these can be combined into one characteristic partial differential equation. Finally, we use this equation in order to simulate the CMB of a toy Bianchi V example and produce its power spectrum. We close with a discussion, and suggestions for further research.

We investigate a scalar-vector-tensor theory in which matter is minimally coupled to a Jordan-frame metric, while a massive vector sector interacts with the baryonic current. We show that the conformal scalar coupling modifies the physical expansion rate measured by matter observers, leading to a late-time enhancement of the effective Hubble constant. By constructing a phenomenological scalar evolution that becomes relevant only at low redshifts, the model provides a purely late-time mechanism for alleviating the Hubble tension without significantly affecting early-universe cosmology. The scalar potential naturally acts as a dynamical dark-energy sector, while the vector contribution behaves effectively as a pressureless component at cosmological scales through a density-dependent vector mass. Hence, the framework connects late-time scalar dynamics, effective dark-energy evolution, and Hubble-tension alleviation within a unified setup. Finally, local gravitational constraints can be suppressed through a chameleon-type screening mechanism, allowing the theory to remain compatible with Solar-System tests while retaining nontrivial cosmological effects.

We construct a five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. We show that the Gauss-Bonnet term removes the local curvature singularity, yielding finite curvature invariants throughout the spacetime, provided the rotation parameter remains below a certain value set by the Gauss-Bonnet coupling. To our knowledge, this is the first analytic example of a singly rotating five-dimensional solution in this framework with finite curvature invariants over a nontrivial region of parameter space. We analyze the geometry across this space, identifying regular, singular, and marginal regimes. Finally, we study the thermodynamic properties, finding that while higher-derivative corrections regularize the local curvature behavior, they also introduce unique challenges to the standard thermodynamic description of Killing horizons.

We point out that a simple late-time cosmological model where our Universe can absorb "baby universes" explains the exponential expansion of our universe without the need of a cosmological constant and leads to a z-dependence of the parameter w(z) in the equation of state. In this model w(z) is less than -1 for z sufficiently large.

Using the post-Newtonian effective field theory (PN-EFT) formalism for spinning gravitating bodies, we derive the next-to-leading-order (NLO) spin-orbit potential and Hamiltonian for a system of N spinning bodies in general relativity. This extends the EFT treatment of the binary case to arbitrary N. We present two derivations: one in the generalized canonical gauge, and one based on the covariant spin supplementary condition (SSC), followed by a noncanonical transformation to canonical variables. In both approaches, the only new contributions beyond the binary case are three-body interaction diagrams. The canonical Hamiltonians obtained from the two EFT routes agree with the known ADM N-body Hamiltonian of Hartung and Steinhoff up to a canonical transformation.

We prove that any background-inert perturbative coupling $ \lambda $ in coincident $ f(Q) $ gravity exhibits a degeneracy with the clustering amplitude $ \sigma_{80} $, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a more deeper $ A_s-D_0(\lambda) $ degeneracy between the primordial amplitude $ A_s $ and the present day growth factor $ D_0(\lambda) $. We outline a consistency check scheme, applicable to models even outside the $ f(Q) $ class, by computing $ A_s $ needed to reproduce the $ \sigma_{80} $ predicted by the sampler. We perform our analysis with two dataset pipelines, based on the coupled/decoupled $ f\sigma_8(z) $ data. To ensure theoretical diversity, we include $ \Lambda $CDM and the Hybrid model in the $ f(Q) $ framework. Our results illustrate that adding the $ \lambda_0\sqrt{QQ_0} $ correction to the models inflates $ \sigma_{80} $ to unphysical values, while showing moderate evidence in favor of the said models. However, this results in an increase of $ 20\%-30\% $ in $ A_s $ in $ 1.7\sigma-2.2\sigma $ tension with Planck values. We utilize the $ 1\sigma $ $ \ln(A_s) $ constraints from Planck as priors in order to fix the artificial increase in $ \sigma_{80} $ and find that all the constrained parameters return to their baseline values. Each model is penalized by around $ 2 $ units per extra parameter. Interestingly, the $ \Lambda $CDM$ +\lambda_0+\ln(A_s) $ + SDSS DR16 combination shows a weak preference over the vanilla $ \Lambda $CDM model, validated by the values of $ \log\mathcal{Z},\;AIC,\;DIC, $ and BIC.

We construct families of deformations of the double-scaled SYK (DSSYK) model and investigate their bulk interpretation. We introduce microscopic deformations of the SYK model which, after ensemble averaging and in the double-scaling limit, are described by a transfer matrix encoding the recurrence relations of basic orthogonal polynomials in the q-Askey scheme. For certain families of deformations in the semiclassical limit at finite temperature, the chord number (encoding Krylov complexity) corresponds to the length of an Einstein-Rosen bridge connecting an End-Of-The-World brane to an anti-de Sitter asymptotic boundary. By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels, signaling a new geometric transition in sine dilaton gravity. Via the SYK-Schur duality, Krylov complexity also admits a representation-theoretic interpretation as the spread of the SU(2) spin in the index of an $\mathcal{N}=2$ SU(2) gauge theory. We study the operator algebras of the deformed theories. The algebras can be type II$_1$ or type I$_\infty$ factors, depending on the operators that are included. The entanglement entropy between the type II$_1$ algebras for a pure state manifests as an extremal surface through the Ryu-Takayanagi formula. We discuss connections between our results and the emergence of baby universes in the bulk.

The recent success of gravitational-wave (GW) astronomy together with renewed plans for lunar geophysical instrumentation has revived interest in using the Moon as a resonant detector for mid-frequency (mHz-Hz) GWs. In realistic observational scenarios, the GW strain amplitude is expected to be constrained independently by networks of GW detectors, which motivates an inverse, \emph{tomographic} question: to what extent can measurements of the Moon's seismic response to known GWs be used to infer its internal structure? In this work, we develop a first-principles, perturbative framework that maps spherically symmetric perturbations of the elastic and density structure to measurable changes in observables, especially GW-driven modal amplitudes of the Moon. The formalism combines (i) a normal-mode representation of the elastic response, (ii) first-order perturbation theory for eigenvalues and eigenfunctions, and (iii) a linearized observation model that links frequency and amplitude observables to model parameters (bulk and shear moduli, density, and interface locations) and their perturbations. We show that the estimation errors of the Moon's elastic parameters can be reduced by about an order of magnitude with observations of calibrated GWs.

We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein gravity, expected to give the leading contribution to the wave-function norm. We demonstrate that the fully gravitational hyperbolic ball partition function, where the boundary fluctuates, develops a nontrivial one-loop phase of $(\mp i)^{D+1}$, analogous to that of the sphere partition function in dS gravity. By contrast, the partially frozen partition function, where the boundary is fixed, remains real and positive. Motivated by this AdS comparison, we conversely investigate a partially frozen dS sphere partition function where the metric on an equator is fixed, finding that its one-loop phase cancels nontrivially. Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.

We study quantum mechanics of bosonic multi-matrix Lagragians in the collective field framework, with particular emphasis on three matrix models. We derive the effective Hamiltonian of the collective field and study the vacuum solution and its stability.

In this work, we perform Markov Chain Monte Carlo (MCMC) analyses using the Planck 2018 cosmic microwave background (CMB) datasets, including temperature, polarization, and lensing, in order to compare matter bounce models with observational data. The particular model we considered contains a scalar field with an exponential potential, which behaves as dust in the asymptotic past of the contracting phase, it realizes a quantum bounce, and then behaves as a transient dark energy field at large scales in the expanding phase. The parameter $\lambda$ appearing in the exponential potential is directly related to the model's scalar spectral index, $n_s$, which is set free in the MCMC analyses, as well as the deepness of the bounce, which controls the amplitude of the power spectrum. We provide constraints on the cosmological parameters and compare the model's performance against the standard inflationary $\Lambda$CDM scenario. Our results indicate that Planck data alone cannot favor one model with respect to the other, showing that the model we investigate can be a viable alternative to inflation.

This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi framework is developed for the symmetric restriction of the theory. Localized topological solutions are found. Their stability, which would normally be prevented in higher dimensions due to scaling instability, is made possible by the presence of an explicit radial dependence on the potential. The first-order equations give rise to an integrable orbit equation which can be used to solve the problem completely. It is shown that target space orbits - but not the solutions themselves - are shared between analogous systems defined in different backgrounds. Moreover, the first-order equations can be mapped into a one-dimensional BPS theory through a transformation encoded by a function $\xi(r)$. The internal structure, size and existence of defects follows from the properties and range of this mapping. We use these tools to evaluate the effect of geometry on confinement, existence, and structure of solitons. Exact solutions are provided in Minkowski, Schwarzschild, de Sitter, Schwarzschild de Sitter and conformally flat backgrounds.

Atom interferometers represent a promising approach for gravitational wave detection in the decihertz frequency band, complementary to existing light-based detectors. The South Pole offers unique advantages for such experiments: exceptionally low seismic noise, established infrastructure for large scientific projects, and a location that strengthens gravitational wave source localization through global triangulation. Here we discuss the scientific case and practical considerations for deploying a long-baseline atom interferometer at the South Pole, which has the potential to expand the global network of gravitational wave detectors while enabling precision tests of fundamental physics.

We study the linearized scattering of dilaton-graviton waves from a thin brane in three-dimensional spacetime. Holographically, the setup models scattering from an interface in a family of strongly coupled theories related to dimensional reductions of higher-dimensional $AdS_{d+2}$ gravity. Unlike the pure $AdS_3$ case, for $d>1$ the physical bulk mode allows incident radiation to be redistributed into reflected, transmitted, and evanescent components. For the $d=2$ background, we obtain a controlled solution in which the interface acts like a rough translucent window, producing diffuse angular scattering and absorption into surface modes. From the dual perspective, the scattering process is suggestive of dissipative flow toward the infrared. For $d=4$, the same analysis reveals a sensitivity to the infrared boundary condition, suggesting that the singular zero-temperature geometry must be regulated in order to have a well-defined scattering process. The structure of the equations nevertheless suggests that a regulated $d=4$ problem may exhibit the same qualitative redistribution of incident flux.

We study the $\alpha'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruipérez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruipérez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $\alpha'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $\alpha'$. We also show that, at zeroth order in $\alpha'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $\alpha'$ corrections to these solutions.

In the shallow water approximation, the cross-sectional profiles of laboratory rivers satisfy a differential equation here shown to be formally the Friedmann equation of cosmology ruling the evolution of Anti-de Sitter universe. The ensuing cosmic analogy provides a counterintuitive Lagrangian for the transverse river profile. Extremizing the corresponding action corresponds to extremizing the friction force on the river bottom and the energy dissipation rate. Analysis of the second variation establishes that this extremum is a maximum.

A consistent non-compact axion cosmology requires a non-periodic field, an effective field theory valid sufficiently above the inflationary scale, and a small non-QCD contribution to the potential that tilts the axionic vacuum landscape in order to trigger a timely domain-wall collapse. All conditions can be met by the dilaton -- the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance.

In the Kerr-Schild double copy, static and spherically symmetric black hole solutions of general relativity are mapped to purely electric solutions of Maxwell's theory in flat spacetime. We demonstrate that, for these configurations, the thermodynamic Smarr formula is structurally identical to the single-copy Gauss's law. Extending this to asymptotically anti-de Sitter spacetimes, we prove that the thermodynamic pressure-volume term ($PV$) naturally emerges from a gauge-theoretic background subtraction. This relationship establishes a novel connection between the classical double copy and black hole thermodynamics.

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that -- within a fixed asymptotic charge sector -- the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.

In this essay we examine the gravitational collapse of a nonrelativistic charged perfect fluid interacting with a dark energy component. Given a simple factor for the energy transfer, we obtain a nonsingular interior solution which naturally matches the Reissner-Nordström-de Sitter exterior geometry. We also show that the interacting parameter is proportional to the overall charge of the final black hole thus formed. For the case of quasi-extremal configurations, we propose a statistical model for the entropy of the collapsed matter. This entropy extends Bekenstein's geometrical entropy by an additive constant proportional to the area of the extremal black hole.

The Minkowski vacuum is often presented in textbooks and reviews as a thermofield double (TFD) state, an entangled state of field modes in the left and right Rindler wedges. This picture is widely used to explain the Unruh effect, motivate entanglement entropy calculations, and connect quantum field theory to black hole thermodynamics and AdS/CFT. However, we show that this interpretation, while elegant, is not exact. We explicitly compute two-point functions and their derivatives for a massless scalar field in two-dimensional Minkowski space, comparing results obtained from canonical quantization with those obtained by assuming a TFD form of the vacuum. Mixed-derivative correlators agree perfectly, but higher-derivative correlators show systematic mismatches that persist even for points well away from horizons and are not removed by infrared regularization. To further test this picture, we construct an alternate coordinate system that divides Minkowski spacetime into two disconnected regions, apply the same derivation that leads to the standard TFD expression, and obtain a new "entangled-state" representation of the vacuum that is not thermal. This demonstrates that the appearance of a TFD structure is a feature of the derivation method rather than a fundamental property of the vacuum. Our results clarify the limits of interpreting the Minkowski vacuum as a literal TFD state, emphasizing that while it captures key thermal features, it should be viewed as a powerful calculational tool rather than a precise statement about Hilbert space structure.

The asymptotically flat, electrically charged, rotating black holes (BHs) in Einstein-Maxwell-dilaton (EMd) theory are known in closed form for \textit{only} two particular values of the dilaton coupling constant $\gamma$: the Einstein-Maxwell coupling ($\gamma=0$), corresponding to the Kerr-Newman (KN) solution, and the Kaluza-Klein coupling ($\gamma=\sqrt{3}$). Rotating solutions with arbitrary $\gamma$ are known only in the slow-rotation or weakly charged limits. In this work, we numerically construct such EMd BHs with arbitrary $\gamma$. We present an overview of the parameter space of the solutions for illustrative values of $\gamma$ together with a study of their basic properties. The solutions are in general KN-like; there are however, new features. The data suggest that the spinning solutions with $0<\gamma<\sqrt{3}$ possess a zero temperature limit, which, albeit regular in terms of curvature invariants, exhibits a $pp$-singularity. A different limiting behaviour is found for $\gamma>\sqrt{3}$, in which case, moreover, we have found hints of BH non-uniqueness for the same global charges.

We present a comprehensive investigation of the F-statistic method for parameter estimation of gravitational wave (GW) signals from compact binary coalescences. By analytically maximizing the likelihood over the luminosity distance and polarization angle, this approach reduces the dimensionality of the parameter space to enhance computational efficiency. We also introduce a novel formulation for calculating the Bayesian evidence for the F-statistic, enabling a quantitative assessment of its performance against standard full frequency-domain (FFD) Bayesian inference. Applying these two methods to analyze several representative GW events (GW190412, GW190814, and GW170817), we find that the F-statistic consistently yields results in good agreement with the FFD approach, while offering a significant reduction in computational cost. We demonstrate that including calibration uncertainty generally improves the agreement between the two methods. Furthermore, under the assumption of physical priors, the F-statistic-based analyses consistently yield higher Bayesian evidence than the corresponding FFD analyses. While the F-statistic produces slightly broader constraints on some parameters, we argue this represents a more honest uncertainty quantification, particularly in high-dimensional parameter spaces with complex posterior structures. These results highlight the significant advantages of the F-statistic method for GW data analysis, positioning it as a powerful tool for the era of high-rate detections with future observatories.

We argue that a high pressure phase transition of relativistic matter to a state with negative energy density, which leads to the formation of horizonless, globally unitary black hole mimickers, also gives rise to the appearance of ``little red dots''. The energy source for the dots is the release of latent energy from the phase transition, and their excess redness is a result of this release taking place in a central region of exponentially small positive $g_{00}$, and hence very high gravitational redshift.

The tidal deformation of compact objects, characterised by their Love numbers, provides insights into the internal structure of neutron stars and black holes. While static bosonic tidal Love numbers vanish for black holes in general relativity, it has been recently revealed that static fermionic tidal perturbations can induce non-zero Love numbers for Kerr black holes. In this paper, we investigate the response of the Reissner-Nordström black hole to the fermionic Weyl field. As a result, we find that the corresponding fermionic tidal Love numbers are also non-vanishing for the Reissner-Nordström black holes except for the extremal ones, which highlights the universal distinct behavior of the static fermionic tidal Love numbers compared to the bosonic counterparts.

We discuss how to model the surface of celestial bodies (such as stars) in quantum gravity to ensure the regularity of quantum corrections to classical solutions of general relativity at the surface of such bodies. Specifically, we use the Vilkovisky--DeWitt unique effective action to calculate universal quantum corrections to the exterior metric for a class of stellar models. Previous descriptions, obtained via a Heaviside density profile, are ``pathological'' at the surface of the star due to the divergence of the metric functions and associated curvature invariants. Introducing a modified version of the Tolman VII density profile, we determine the minimal degree of differentiability required for this function to generate regular quantum corrections at the star's surface.

The purpose of this article is to compute the asymptotic charges of a vacuum solution to the Einstein field equations describing a naked singularity with a non-vanishing quadrupole moment, known in the literature as the Zipoy-Voorhees spacetime (q-metric). In addition to the well-known asymptotic quantities such as the Bondi-Sachs energy-momentum, the BMS charges and NP constants of this spacetime are computed. Explicit calculations of the latter are relatively scarce in the literature. Moreover, it has been proven that the NP constants of asymptotically flat, stationary, vacuum, and algebraically special spacetimes vanish (for instance, those of the Kerr spacetime). A by-product of the present analysis is to show that the algebraically special condition in the aforementioned result appears to be crucial, since the q-metric provides a counterexample to the conjecture that all asymptotically flat, stationary, vacuum, and asymptotically algebraically special spacetimes (a weaker version of the algebraically special condition) have vanishing NP constants.

We investigate some cosmological implications at background level of the Bumblebee model. The phase-space, the critical points and their stability are analyzed in detail applying well-established dynamical system techniques. What is more, upon comparison to available supernovae data, the best fit numerical value of the unique free parameter of the model is determined. We show graphically all the cosmological quantities of interest versus red-shift, such as the deceleration parameter, dark energy equation of state parameter, etc. The statefinders and the age of the Universe are also computed. Finally, a comparison to the $\Lambda$-CDM model is made as well.

We propose a general framework for the study of asymptotically flat spinning dyonic {\it extremal} black holes (eBHs) in $D=4$ Einstein-Maxwell-dilaton theory. Restricting to the stringy value $\gamma=1$ of the dilaton coupling constant, we report on the existence of a one parameter family of eBHs which are free of pathologies, provided their magnetic and electric charges are equal. An understanding of this condition is found from a study of the near horizon limit of the solutions, both perturbative closed form and numerical solutions being presented.

We investigate metric perturbations of a spherically symmetric black hole in higher curvature gravity. We show that higher curvature corrections deform the near-horizon region of the effective potential, and that the deviations of the quasinormal mode (QNM) frequencies from their general relativity (GR) values become more pronounced for overtone modes. We find that, as the order of the higher curvature term increases, the deformations approach the horizon and the deviations of the overtone QNM frequencies grow progressively larger. We also analyze the ringdown waveforms in the higher curvature gravity model. We consider setups in which the deviations from the vacuum-GR QNMs remain mild for the fundamental mode and the first few overtones, and show that these shifted QNMs can be identified in the ringdown signal through waveform fitting.

We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe the evolution of orbital parameters in strong gravity relativistic settings. As examples of external forces we considered Kerr and $q$-metric space-times generated forces, for which we solve equations for osculating elements in linear approximation. For the Kerr space-time in the post-Newtonian limit, our result reproduces the well-known Lense--Thirring precession of the longitude of the ascending node.

In this paper, we investigate the equilibrium configurations and radial perturbations of neutron stars within a subclass of gauge-invariant Scalar-Vector-Tensor (SVT) theories. By solving the generalized Tolman-Oppenheimer-Volkoff (TOV) equations for several values of the modified gravity parameter, we examine the impact of the vector-curvature coupling on the structure and properties of neutron stars. We then extend our analysis by deriving the quadratic action governing linear radial perturbations and computing both the normal modes associated with the matter sector and the scalar quasinormal modes arising from the additional propagating degree of freedom of the theory, which is able to propagate outside the neutron star. Our results show that the modified gravity parameter can significantly affect the mass-radius relation, the oscillation spectrum, and the stability properties of neutron stars, while preserving the coincidence between the onset of radial instability and the maximum-mass configuration, as in General Relativity.

This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincaré and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent numerical analyses of central configurations--special equilibrium solutions to the Newtonian $N$-body problem--we uncover systematic spatial variations in nearest-neighbor particle separations correlated with the radial distance from the system's center of mass. We argue that these variations reflect a context-dependent, emergent effective geometry shaped by gravitational interactions, in accordance with Poincaré's assertion that measured geometry depends on the forces influencing measuring devices, and Einstein's view that rods and clocks define physical geometry through their local dynamics. By revisiting these foundational insights within a modern computational framework, we provide evidence that geometry in self-gravitating Newtonian systems is not a fixed background, but an emergent construct arising from internal physical interactions.

Chaplygin gas and other k-essence models exhibit emergent geometry, with perturbations propagating on an acoustic metric disformally related to the Einstein-frame metric. For superluminal sound speed, we identify the disformal metric as the "causal frame," since choosing a finite causal-frame lapse yields hyperbolic equations of motion for fields propagating in either frame. We show that with a phantom Chaplygin gas, the Einstein-frame lapse is forced to pass smoothly through zero and change sign while the causal-frame lapse remains positive. As a result, Einstein-frame degrees of freedom (including the scale factor) undergo spontaneous time-reversal while the Chaplygin gas evolves monotonically, enforcing a robust non-singular bounce even in the presence of additional matter canonically coupled to the Einstein frame.

We investigate the shadows, accretion disks, and observational images of rotating Ayón-Beato-García black holes characterized by mass $ M $ , spin $ a $ , and electric charge $ \zeta $ . Our analysis reveals that the shadow size decreases with increasing $ \zeta $, and in near-extremal configurations (e.g., $ a = 0.95 $), the shadow adopts a distinctive ``D''-shaped morphology. For the accretion disk, we extend its inner edge to the event horizon and account for distinct particle dynamics inside and outside the innermost stable circular orbit (ISCO). We find that the correlation between $ (a, \zeta) $ and the observer's inclination angle significantly influences image asymmetry and inner shadow distortion. At higher inclinations, the direct and lensed images separate, forming a hat-like structure. Additionally, we compute the redshift distribution of the disk's direct and lensed emissions under varying parameters and viewing angles. By comparing theoretical shadow diameters with the Event Horizon Telescope observations of M87 $^{*}$ and Sgr A $^{*}$--using inclination angles of $17^{\circ} $, $ 50^{\circ} $, and $ 90^{\circ} $--we constrain the viable parameter space, yielding the joint bound $0.132811\,M < \zeta < 0.213607\,M$ consistent with both sources.

The point-particle approximation is foundational to modelling clustering of matter in the universe, but is fundamentally inconsistent within General Relativity due to associated spacetime singularities. This bottleneck has historically restricted the study of matter clustering to linear scales. We resolve this by utilising the recent observation that a matter horizon precedes the formation of caustics in expanding spacetimes. This allows for the isolation of singularities via spacetime surgery. By glueing distinct spacetime sheets related by a discrete transformation across the shared boundary, we derive a covariant backreaction term that contributes to the effective energy-momentum tensor. Crucially, we identify this backreaction contribution with gravitational edge modes; physical degrees of freedom residing on boundaries that arise from the breaking of the diffeomorphism group. These gravitational edge modes modify local particle trajectories, naturally producing flat galaxy rotation curves in the outskirts without invoking dark matter particles. Our framework thus demonstrates that gravitational edge modes can act as effective dark matter, offering a first-principles alternative to particle dark matter for explaining galactic dynamics.

The paper develops a model to understand the effective quantum geometry of a black hole horizon and the emission of Hawking spectrum in $2+1$ dimensions. Using the algebra of Hamiltonian charges on the horizon, we establish that one should view the black hole horizon as formed out of quantised lengths of elementary quanta of value $8\pi \ell_{P}\, n$, where $n\in \mathbb{N}$, and $\ell_{P}$ is the Planck length. We determine the black hole entropy using this equidistant length spectrum in the microcanonical ensemble and show that its value is close to the Bekenstein-Hawking entropy. To evaluate the Hawking spectrum, we note that, to an observer near the black hole horizon, the entropy (or length of horizon cross-section) is related to the black hole energy. Hence, one may develop a formulation of length ensemble (similar to the area canonical ensemble of Krasnov) from which the black body spectrum may be obtained directly. This local observer perceives a Hawking spectrum whose temperature is modified by the Tolman factor.

Inspired by Mashhoon's framework connecting black hole quasi-normal modes (QNMs) to bound-state resonances in inverted potentials, V$\ddot{\text{o}}$lkel's recent numerical analysis of asymptotically flat Schwarzschild black holes revealed a counterintuitive phenomenon: highly excited bound states rapidly delocalize, become extremely weakly bound, and exhibit wavefunctions highly sensitive to far-field perturbations. To analytically explain this phenomenon and extend the investigation to Schwarzschild-de Sitter (SdS) black holes, we derive the characteristic equation for excited bound-state resonances in SdS spacetime and obtain compact closed-form analytical expressions for their resonance energies. In the $\Lambda\rightarrow 0$ limit, our SdS-derived spectrum aligns perfectly with recent results for Schwarzschild black holes. We analytically demonstrate that the rapid and infinite delocalization of highly excited resonances is a universal feature of asymptotically flat Schwarzschild systems. More significantly, we prove that SdS black holes support only a finite number of bound-state resonance levels -- in sharp contrast to the infinite spectrum of the asymptotically flat case. This finiteness implies an upper bound on the oscillatory domain of the resonance eigenfunctions in SdS geometries, thereby preventing infinite delocalization and offering a fundamental distinction in the resonance structure of black holes in different asymptotic backgrounds. Surprisingly, we also find that delocalized half-bound states exist in SdS black holes when the $\Lambda$ takes specific discrete values. This is a unique feature of SdS black holes and is absent in asymptotically flat Schwarzschild black holes. We also reveal the deep connection between half-bound states and the number of bound-state resonance energy levels.

Schwarzschild black holes are expected to emerge as the end states of the classical gravitational collapse from non-singular configurations. After integrable curvature singularities appear, the interior geometry can be modelled to exhibit a transition, called ``Minkowski breaking'', when the inner horizon disappears, before all matter collapses into the central singularity. This picture implies a quantum framework to describe the final stages of the gravitational collapse, and here we will provide more insights from the semiclassical approximation for the energy-momentum tensor and the Madelung approximation for collapsing matter. In particular, we will show that the quantum potential in the Raychaudhuri equation starts to strongly oppose the collapse towards the Schwarzschild singularity precisely after the Minkowski breaking.

The inflationary Lyth bound relates the primordial tensor amplitude to the inflaton field excursion. There is no analogous universal relationship in the case of ekpyrotic, bouncing, and cyclic models because scalar and tensor perturbations depend on entropy conversion, matching through the bounce and the specific mechanism that violates or evades the null energy condition. Nevertheless, the background kinematics fulfills a useful non-inflationary analogue: a field-space distance budget. In this study, we propose a phase-resolved distance criterion for a non-inflationary smoothing process and decompose the invariant scalar distance into ekpyrotic smoothing, entropy-to-curvature conversion, bounce, and post-bounce contributions. Then, we impose BKL anisotropy suppression as an additional constraint on the ekpyrotic phase. In the canonical phase of the ekpyrotic contraction, we recover the known small-field scaling and generalize it to total budget inequality. We impose three requirements: a BKL (Belinski-Khalatnikov-Lifshitz) anisotropy suppression that is parameterized separately, a phenomenological cutoff-corrected distance budget inspired by tower of states logic, and observational conversion windows from residual isocurvature and non-Gaussianity. Furthermore, we propose a new master condition that provides a lower bound on the value of the parameter $\epsilon_{\rm ek}$ that depends on the remaining distance available after conversion and the cosmological bounce. We also derive a curvature constraint for scale-invariant entropy perturbations in curved field space which shows that the small total distance and the observed red tilt seem to indicate ultra-fast-roll ekpyrosis, sharp turns, short or strongly modified bounces, and/or significant negative sectional curvature of the scalar manifold. Finally, we demonstrate methods for testing the distance budget against observational data.

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 the decoupling limit for single-field ultra slow-roll (USR) inflation and obtain a non-perturbative Hamiltonian in terms of the Goldstone field $\pi$. To complete the dictionary, a non-linear relation between the curvature perturbations and $\pi$ is presented. Using these results, we compute higher-order loop corrections in USR models with a sharp transition to the attractor phase, relevant for PBHs formation. It is shown that in the idealized picture in which the transition from the USR phase to SR phase is instantaneous and sharp, the loop corrections on long CMB scales increase rapidly with the number of loops $L$ and the setup may go out of perturbative control.

We calculate the action and the interaction Hamiltonians to all orders in perturbation theory in the model of single field inflation with a transient ultra slow-roll phase. Employing the formalism of EFT of inflation, we obtain a compact non-perturbative expression for the interaction Hamiltonian in terms of the Goldstone field $\pi$ in the decoupling limit. In addition, we also present a non-linear relation between $\pi$ and the curvature perturbations to all orders in perturbation theory. These are powerful results which enable us to calculate the cosmological correlators and loop corrections to any order in perturbation theory. As a non-trivial example, we calculate the $L$-loop corrections on long CMB scale perturbations in the USR models which are used for PBHs formation. We show that the loop corrections scale like $(\Delta N {\cal P}_e L) ^L$ in which ${\cal P}_e$ is the peak of the power spectrum and $\Delta N$ is the duration of the USR phase. This indicates that the loop corrections grow quickly out of perturbative control for large values of $L$. In the conventional USR setup for PBHs formation with $\Delta N \simeq 2.5$, this happens at $L=4$.

Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and connect to the sum-over-histories approach by clarifying the Hilbert space interpretation of various gravitational path integrals. We use one-dimensional (or mini-superspace) models as the simplest context to exemplify the conceptual ideas. We emphasise that a physical Hilbert space can be defined either by requiring states to be annihilated by constraint operators (e.g., the Wheeler-DeWitt equation) or by equivalence relations between wavefunctions, and explain that these two approaches are related by an inner product. We advocate that the group averaging procedure constructs the correct physical inner product. The Klein-Gordon inner product is not positive-definite, which we explain as arising from a bad gauge choice; nonetheless, it agrees with group averaging when such a problem is absent. These concepts are all embedded in the BRST/BFV formalism, which provides a systematic way to construct these and other physically equivalent inner products (e.g., from maximal-volume gauge and Gaussian averaged gauges). Finally we discuss the application of these ideas in the semi-classical approximation, including non-perturbative gravitational effects.

It has recently been shown that the Nambu-Goto equation for a string emerges from the junction conditions in three-dimensional gravity. Holographically, gravitational junctions are dual to interfaces in conformal field theory. We demonstrate at the level of linearized gravitational perturbations that each stringy mode of the junction corresponds to a $\mathcal{H}_{in}\rightarrow \mathcal{H}_{out}$ quantum map which can be factorized into a scattering matrix involving reflection/transmission and a relative automorphism of the Virasoro algebra, and also a $\mathcal{H}_{L}\rightarrow \mathcal{H}_{R}$ map of similar nature. These maps preserve the conformal boundary condition, are independent of the background conformal frame, as in the case of conformal interfaces studied in the literature, and realize a tunable energy transmitter.

We demonstrate that $n$-way junctions in three dimensional gravity correspond to coupled $n-1$ strings each satisfying the Nambu-Goto equation in the smoothened background, and with sources consisting of Monge-Ampère like terms which couple the strings. For $n\geq 3$, these $n-1$ degrees of freedom survive the tensionless limit implying that matter-like behavior can arise out of \textit{pure} gravity. We interpret these stringy degrees of freedom of gravitational junctions holographically in terms of wavepackets which collectively undergo perfect reflection at the multi-interface in the dual conformal field theory.

Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK). First, we demonstrate that the growth rate of Krylov state complexity corresponds to the wormhole velocity, and show that its expectation value in coherent states serves as a boundary diagnostic of firewall-like structures via bulk reconstruction. We also delineate an alternative bulk description in terms of the proper momentum of an infalling particle at early times, establishing a threefold duality between the Krylov complexity growth rate, wormhole velocity, and proper momentum, with clear regimes of validity. Beyond the first moments, we argue that higher-order Krylov complexities capture connected bulk contributions encoded by replica wormholes, while the logarithmic variant probes the replica saddle structure. Finally, within a third-quantized setting incorporating baby universes, we show that the Krylov entropy equals the von Neumann entropy of the parent-geometry density matrix obtained after tracing out baby universes, thereby quantifying information flow into the baby universe sector. Together, these results elevate Krylov-space observables to sharp probes of bulk dynamics and topology in ensemble-averaged 2D gravity.

This paper presents an enhanced methodology for searching long transient gravitational waves associated with a newborn magnetar, with particular focus on the regime in which the early spin-down is dominated by gravitational-wave emission. The analysis is performed using a strongly improved version of the generalized Frequency Hough Transform algorithm, called GFH-v2. We describe the main developments introduced relative to the original implementation and outline the optimized parameter-space selection used in the search. We then compute the theoretical sensitivity of the method and compare it with an empirical sensitivity estimate obtained by injecting simulated signals into LIGO-Virgo-KAGRA O4a data. The updated framework achieves improved sensitivity and computational performance. These results provide a robust basis for future directed searches for long-transient gravitational-wave signals from core-collapse supernovae and other transient events in current and upcoming observing runs.

We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the ultraviolet contributions. The method leads us to identify an apparent difficulty to renormalize with Hamiltonian counterterms within the in-in formalism. We also discuss the importance of the finite parts of loop corrections that can be distinguished from their associated counterterm contributions. As an application, we examine the one-loop primordial bispectrum in the context of the effective field theory of inflation, considering a specific set of interactions, and identifying a contribution distinguishable from its tree-level counterpart.

We propose a novel gravitational mechanism for the non-thermal production of dark matter driven by curvature-induced tachyonic instabilities after inflation. Departing from the commonly studied non-minimal couplings to gravity, our framework considers a real spectator scalar field coupled quadratically to spacetime curvature invariants. We show that the rapid reorganization of spacetime curvature at the end of inflation can dynamically render the dark matter field tachyonic, triggering a short-lived phase of spontaneous symmetry breaking and explosive particle production. As a concrete and theoretically controlled example, we focus on the Gauss-Bonnet topological invariant. By combining analytical estimates with $3+1$ classical lattice simulations in the spectator field approximation, we track the out-of-equilibrium evolution of the system and compute the resulting dark matter abundance. We find that this purely gravitational mechanism can robustly reproduce the observed dark matter relic density over a wide range of masses and inflationary scales, providing also a simple fitting function that enables a lattice-independent application of our results.

It has been proposed that any coupling constant in a covariant action can be treated as a conserved charge by promoting the coupling constant to auxiliary fields, typically realized by a scalar field paired with a higher-form gauge field. However, the procedure may break local symmetries, which can be explicitly shown in a simpler setting such as Maxwell theory. The Hamiltonian analysis of Maxwell theory with the auxiliary fields reveals that some of the constraints are second-class. Applying the BFT formalism, we restore the broken local symmetries and obtain a fully symmetric action defined on an extended configuration space. Despite the restoration of the local symmetries, no additional conserved charges are associated with the recovered symmetries. Consequently, the original theory turns out to be the gauge-fixed version of the extended theory.

Conservation of super-horizon tensor fluctuations is crucial for connecting inflation to observations. Starting from first principles, recent works have found violations of this conservation if free-streaming radiation is produced during reheating. We show that the non-conservation is sensitive to the radiation initial state, and argue that the physical state should be affected by tensor perturbations that are already present during reheating. The deviation from super-horizon conservation is then negligible, recovering the standard result from kinetic theory. In contrast, a globally homogeneous and isotropic plasma state leads to a large suppression of tensor amplitudes. This difference between the local (physical) and global thermal equilibrium settles the discrepancy between the older and recent literature.

Sign-switching dark energy provides a novel mechanism for modifying the late-time expansion history of the Universe without invoking additional fields or finely tuned initial conditions. In this work, we investigate a class of background--level cosmological models in which the dark energy contribution changes sign at a transition redshift $z_\dagger$, producing a sharp deviation from standard $\Lambda$CDM dynamics. We confront these models with a comprehensive set of cosmological observations, including Planck 18 cosmic microwave background (CMB) measurements, DESI DR2 Baryonic Acoustic Oscillation (BAO) data and the Pantheon+ $\&$ SH0ES Type Ia supernova sample (SN). Using a full Markov Chain Monte Carlo (MCMC) analysis, we find that the sign-switching scenario significantly alleviates the Hubble tension while obtaining better results when statistically comparing with $\Lambda$CDM, as quantified by the Akaike and Bayesian information Criteria. Although the model is explored only at the background level, the improvement in the inferred Hubble constant demonstrates that sign-switching dark energy offers a promising and physically economical pathway toward resolving late-universe discrepancies.

In this work we investigate the influence of weak acceleration on the confinement-deconfinement phase transition in gluodynamics. Our study is carried out within lattice simulation in the comoving reference frame of accelerated observer which is parameterized by the Rindler coordinates. We find that finite temperature confinement-deconfinement phase transition turns into spatial crossover in the Rindler spacetime. In other words, spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. We determine the position of the boundary between the phases as a function of temperature for several accelerations and find that it can be described by the Tolman-Ehrenfest law with rather good accuracy although a minor deviation takes place. Moreover, the critical temperature of the system in the weak acceleration regime is found to remain unchanged as that of the standard homogeneous gluodynamics. Our results imply that the spatial confinement-deconfinement transition might take place in the vicinity of the Schwarzschild black hole horizon.

An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational interaction necessarily comes with some level of noise, i.e., non-reversibility. Here, we give a systematic classification of all possible such models consistent with the basic requirements that the non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. We demonstrate that for any such model to be non-entangling, a quantifiable, minimal amount of noise must be injected into any experimental system. Thus, measuring gravitating systems at noise levels below this threshold would be equivalent to demonstrating that Newtonian gravity is entangling. As concrete examples, we analyze our general predictions in a number of experimental setups, and test it on the classical-quantum gravity models of Oppenheim et al., as well as on a recent model of Newtonian gravity as an entropic force.

We propose that the size of the universe and its rate of expansion cannot be simultaneously specified with arbitrary precision, a quantum mechanical statement encoded in a deformed commutation relation for the scale factor. The deformation modifies the Friedmann equation by adding a geometric correction to the expansion rate, and the sign and magnitude of a single free exponent determine the cosmological behavior. When the exponent is positive, the model predicts late-time dark energy with $w > -1$, testable with current and next-generation surveys. When the exponent is sufficiently negative, the same deformation produces a non-singular classical bounce that resolves the Big Bang singularity. The model introduces no new particles or fields and preserves a scale-invariant primordial power spectrum. The deformation has a natural interpretation as a horizon-scale phenomenon, with the cosmological horizon, and not the Planck length, setting its characteristic scale. The late-universe regime is then its generic application, with the expansion history as the primary observable signature. Cosmic acceleration may be the macroscopic imprint of quantum gravity at the cosmological horizon.

We explore the possibility of explaining dark matter through six-dimensional (6D) primordial black holes (PBHs) in a theory with two extra dimensions. Interestingly, in this scenario the fundamental energy scale is of the order of $\sim 10$ TeV, accessible by future experiments. We analyse the viability of charged and rotating 6D black holes under standard Hawking evaporation as well as the memory burden scenario. In the case of pure Hawking evaporation, only PBHs with masses $M > 10^8$ g survive to present, while the lifetime of near-extremal configurations is extended by a factor $1/\beta^{1/2}$, where the parameter $\beta$ characterizes small deviations from extremality. In the memory burden scenario evaporation is enormously suppressed, and sub-gram mass PBHs can survive to the present epoch. At future colliders such as the Future Circular Collider, these micro black holes produce characteristic high multiplicity events, $\langle N \rangle \sim 21$, with thermal spectra, enabling direct probes of the fundamental scale and the number of extra dimensions. We find that the memory burden mechanism opens a broad new mass window for light PBH dark matter, while the Kaluza-Klein mass splitting $\Delta m$ aligns with the atmospheric neutrino scale, suggesting a unified framework between Swampland constraints, cosmology, collider physics, and low energy phenomenology.