The tension between measurements of the Hubble constant $H_0$ locally and the value inferred from Planck satellite have provided a strong motivation to explore theoretical frameworks beyond the standard cosmological model ($\Lambda$CDM). To this aim, we investigate the $H_0$ tension in the Rastall $\Lambda$CDM model (R-$\Lambda$CDM), formulated within the Rastall gravity framework as a phenomenological extension of General Relativity featuring a non-conserved energy-momentum tensor. To constrain the cosmological parameters, we employ a comprehensive combined dataset including Big Bang Nucleosynthesis (BBN), Hubble parameter $H(z)$, Type Ia supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) anisotropies, and the growth rate of cosmic structures $f(z)\sigma_8(z)$. The estimation of model parameters is performed via Markov Chain Monte Carlo (MCMC) sampling within a Bayesian statistical framework. Our results show that the R-$\Lambda$CDM model, especially in closed geometry, reduces the $H_0$ tension, bringing the discrepancy with the local SH0ES measurements down to $1.97\sigma$ to $2.18\sigma$. However, the tension related to the $\sigma_8$ parameter remains unresolved.

A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian limit, but it is not given by the Jüttner distribution commonly employed in relativistic kinetic theory. The nonlinear kinetic diffusion equation on a general Lorentzian manifold is consistent with the contracted Bianchi identities and therefore can be coupled to the Einstein equations of general relativity.

Black holes in General Relativity exhibit a remarkable feature: their response to static scalar, electromagnetic, and gravitational perturbations -- as quantified by the so-called tidal Love numbers -- vanishes identically. We present the first exception to this rule: the Love numbers of a black hole perturbed by a fermionic field are nonzero. We derive a closed-form expression of these fermionic Love numbers for generic spin in the background of a Kerr black hole with arbitrary angular momentum. In contrast, we show that the fermionic dissipation numbers vanish for static perturbations, reflecting the absence of superradiance for fermions. These results highlight a fundamental distinction between bosonic and fermionic perturbations, which can be interpreted as a breaking of the hidden symmetries that underlie the vanishing of Love numbers in the bosonic sector.

We derive an exact solution representing a Bondi-type stationary accretion of a kinetic (Vlasov) gas onto the Kerr black hole. The solution is exact in the sense that relevant physical quantities, such as the particle current density or the accretion rates, are expressed as explicit integrals, which can be evaluated numerically. Whereas the angular momentum accretion rate is shown to vanish exactly, we provide an analytic approximation which allows us to obtain simple formulas for the mass and energy accretion rates. These formulas are used to derive characteristic time scales of the black hole mass growth and the associated spin-down in two different scenarios: assuming that the ambient energy density is either constant or decreases on a cosmological scale.

Extreme-mass-ratio inspirals, where a stellar-mass object orbits a supermassive black hole, are prime sources of millihertz gravitational waves for upcoming space-based detectors. While most studies assume idealized vacuum backgrounds, realistic extreme-mass-ratio binaries are embedded in astrophysical environments, such as accretion disks, stellar clusters, or dark matter spikes, disks and halos, that can significantly alter the orbital dynamics. We explore bound geodesics around general-relativistic solutions describing rotating black holes surrounded by matter halos, for the first time, and map how environmental effects meddle with the spacetime symmetries of vacuum spinning (Kerr) black holes. In particular, we find that the loss of a Carter-like constant leads to geodesic non-integrability and the onset of chaos. This manifests through resonant island and chaotic layer formations around transient orbital resonances in phase space; features that are otherwise completely absent in integrable Kerr geodesics. Resonant islands, which are extended, non-zero volume regions in phase space, encapsulate periodic orbit points. Non-integrability ensures that the periodicity of the central resonant point is shared throughout the island's geodesics, thus effectively enhancing the lifespan of resonances, beyond Kerr-based predictions. Therefore, they can subject distinct imprint on gravitational-wave signals, with significant consequences for gravitational-wave modeling and parameter inference of astrophysical extreme-mass-ratio inspirals.

Gravitational waves from the coalescence of compact objects carry information about their dynamics and the spacetime in regions where they are evolving. In particular, late-time tails and memory effects after the merger are two low-frequency phenomena, not detectable by current instruments, but which can be observed by future detectors. Their low-frequency nature could, in principle, make them more sensitive to larger-scale structures at galactic length scales. We show that indeed there are transient features, such as amplitude changes, in both tails and (linear) memory when the merger occurs while immersed in an astrophysical environment. For realistic galaxies, the environment's compactness is small enough that the effect is strongly suppressed, but these effects could become relevant for mergers occurring in regions with matter overdensities, like the ones recently observed numerically for wave dark matter. On the other hand, the memory (the difference between the amplitude asymptotically early and late) and asymptotically late decay are independent on the properties of the environment.

The (degenerate) geometry of event horizons is linked to Carrollian fluids. We investigate the behavior of event horizons via a perturbative coupling to a massless scalar field, making connections to Carrollian hydrodynamics with a driving source, and discuss the fluid equilibration in tandem with the horizon's relaxation to equilibrium. We observe that after the perturbation dies off, the Carrollian fluid energy and momentum densities approach equilibrium as the horizon asymptotically becomes non-expanding. We connect the equilibration of the Carrollian fluid dual to the black hole horizon through the expansion of its background geometry.

New General Relativity (NGR) is a class of teleparallel theories defined by three free parameters, effectively reduced to two after appropriate normalization, which are subject to experimental constraints. In this framework, matter couples minimally to the metric, ensuring that test particles follow geodesics and that null congruence expansions can be employed to detect local horizons. Assuming such horizons exist, we demonstrate that all physically viable NGR models--including the Teleparallel Equivalent of General Relativity (TEGR) and the one-parameter Hayashi and Shirafuji model (1P-H&S)--inevitably exhibit divergences in torsion scalars at the local horizon. This singular behavior obstructs the interpretation of these models and their associated teleparallel geometries as black hole configurations.

In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks, using a warped region of spacetime in the shape of a bubble that transports particles with mass traveling through spacetime with superluminal speed. Although initial results indicated this scenario as nonphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such a nonphysical situation may not always be true. This thesis presents newfound solutions for the Einstein field equations, considering the Alcubierre warp drive spacetime metrics. The central premise is to study the fluid matter as the gravity source, rather than the more common vacuum or negative energy sources, to explore the potential for generating superluminal velocities, or \textit{warp speeds}, through a warped region in the spacetime. Such solutions have various matter-energy sources: dust particles, perfect fluid, quasi-perfect fluid with anisotropic pressures, charged dust, and a perfect fluid within a cosmological constant spacetime. A connection between some of these solutions featuring shock waves described by a Burgers-type equation with a term on the right-hand side of the equation purely dependent on time is also shown. This could mean warp drives are closely related to vacuum energy and possibly have topological effects such as shock waves.

High-fidelity gravitational waveform models are essential for realizing the scientific potential of next-generation gravitational-wave observatories. While highly accurate, state-of-the-art models often rely on extensive phenomenological calibrations to numerical relativity (NR) simulations for the late-inspiral and merger phases, which can limit physical insight and extrapolation to regions where NR data is sparse. To address this, we introduce the Spinning Effective-to-Backwards One Body (SEBOB) formalism, a hybrid approach that combines the well-established Effective-One-Body (EOB) framework with the analytically-driven Backwards-One-Body (BOB) model, which describes the merger-ringdown from first principles as a perturbation of the final remnant black hole. We present two variants building on the state-of-the-art $\texttt{SEOBNRv5HM}$ model: $\texttt{seobnrv5_nrnqc_bob}$, which retains standard NR-calibrated non-quasi-circular (NQC) corrections and attaches a BOB-based merger-ringdown; and a more ambitious variant, $\texttt{seobnrv5_bob}$, which uses BOB to also inform the NQC corrections, thereby reducing reliance on NR fitting and enabling higher-order ($\mathcal{C}^2$) continuity by construction. Implemented in the open-source $\texttt{NRPy}$ framework for optimized C-code generation, the SEBOB model is transparent, extensible, and computationally efficient. By comparing our waveforms to a large catalog of NR simulations, we demonstrate that SEBOB yields accuracies comparable to the highly-calibrated $\texttt{SEOBNRv5HM}$ model, providing a viable pathway towards more physically motivated and robust waveform models

This paper primarily investigates the optical characteristics of two minimal Schwarzschild black hole deformations - the Kazakov-Solodukhin and Ghosh-Kumar black holes - under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase compared with the Schwarzschild black hole, but those of the latter decrease. The data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. In the case of spherical accretion, the quantum correction of Kazakov-Solodukhin black hole leads to the increase of black hole shadow size and the decrease of integrated intensity, while the shadow size of magnetically charged Ghosh-Kumar black hole decreases and the integrated intensity increases. The shadow radius of the black hole is independent of the spherical accretion models. For an optically and geometrically thin accretion disk, the integrated intensity is mainly contributed by direct emission, and the contributions of photon rings and lensed rings are very small. In addition, the photon rings and lensed rings of Kazakov-Solodukhin black hole are narrower, while those of Ghosh-Kumar black hole are wider. Whereas the Kazakov-Solodukhin black hole exhibits higher brightness, the Ghosh-Kumar black hole shows lower brightness. Additionally, a disk closer to the black hole correlates with a smaller shadow radius. This paper proposes a method to distinguish different black holes in a specific thin disk model.

We compute the canonical (brick wall) entropy of Hawking radiation in a quantum black hole whose exterior is described, to first order in a small quadrupole parameter, by the static $q$-metric, which is an exact vacuum solution of the Einstein equations. Counting near horizon quasinormal modes shows that a modest quadrupolar deformation self-regularizes the ultraviolet divergence: the entropy of Hawking radiation is finite for any non-vanishing quadrupole, without an ad hoc cutoff. Matching this canonical entropy to the Bekenstein-Hawking entropy leads to no-hair violating multipoles, at percent-to-tens-of-percent level, and provides concrete observational targets for the Next Generation Event Horizon Telescope (ngEHT) and the Laser Interferometer Space Antenna (LISA).

The curvature singularity problem in $f(R)$ dark energy models poses a significant challenge to their viability as alternatives to the $\Lambda$CDM paradigm. In this work, we investigate the possibility of resolving this issue by incorporating higher-order corrections that are compatible with the inflationary phase. We analyze the effects of adding $R^2$, $R^{\frac{m+2}{m+1}}$ and $\alpha$-attractor representation in $f(R)$ gravity terms to types of dark energy $f(R)$ models, focusing on their ability to prevent singularities in high-density environments. Our results demonstrate that these corrections can effectively stabilize the models, ensuring their consistency across both inflationary and late-time cosmological scales.

We investigate dynamics of the conformal scalar equation with defocusing cubic nonlinearity and Robin boundary conditions on the Reissner-Nordström-anti-de Sitter background. At certain parts of the parameters phase space the zero solution ceases to be stable. We present two mechanisms responsible for this phenomenon.

Amazingly, recent studies indicate that nonlinear effects are of great significance for modelling black hole ringdown. Transient electromagnetic events in the astrophysical environment are typically high-energetic, potentially responsible for some nonlinearities in ringdown. Motivated by the desire to understand these nonlinearities, we solve the inhomogeneous Bardeen-Press-Teukolsky equation numerically, and find second-order gravitational tails induced by an electromagnetic source. Our results suggest that the second-order tails of curvature perturbations with multipole numbers $l\geq4$ decay as $t^{-2l-2}$ at fixed spatial position and $u^{-l-3}$ in retarded-time $u$ at null infinity, slower than their linear counterparts, which can play a role in multi-messenger observations.

We investigate the gravitational memory effect in the full Generalized Proca gravity, the most general metric theory including a gravitational Proca field with derivative self-interactions that still maintains second-order equations of motion. Building on our previous works on memory in other massless and massive metric theories, we extend a unified framework for computing displacement memory and apply it to Generalized Proca gravity. We identify two non-trivial physically distinct classes of background conditions of Generalized Proca theory within the assumption of asymptotic flatness: a Lorentz-invariant but massive case, and a Lorentz-violating, massless case. The former exhibits dispersive scalar and vector modes and allows a Horndeski-like treatment of memory, while the latter resembles the asymptotic dynamics of Einstein-Æther theory including the same Lorentz-breaking effects on displacement memory. In both cases, we derive the fully gauge invariant and dynamical second order action, derive the effective stress-energy tensor and study its contribution to the memory integral. We highlight the distinction between phase and group velocity in the tensor memory formula sourced by dispersive propagating modes. Finally, we re-emphasize how observational constraints on Lorentz violation may be imposed by the structure of the memory signal.

In this work, we investigate bound periodic orbits of timelike particles in the spacetime of dyonic black holes arising from quasi-topological electromagnetic theory. By varying the coupling parameter $\alpha_1$, the corresponding black hole solutions exhibit diverse horizon structures, including naked singularities and black holes with one to four horizons. We find that for sufficiently small $\alpha_1$, the metric function $f(r)$ becomes non-monotonic outside the event horizon in spacetimes with one or two horizons, while in all other cases, $f(r)$ remains strictly monotonic. In the non-monotonic regime, the radial effective potential develops a double-barrier structure, allowing the emergence of multiple marginally bound orbits and multiple branches of periodic orbits associated with the same rational number $l$. Although differing in radial structure, these orbit branches are topologically equivalent. Remarkably, when the outer potential barrier exceeds unity, bound orbits with energy $E>1$ become possible, in addition to the standard $E<1$ branches. When the peak reaches $E=1$, up to three distinct bound orbit branches may coexist. We also identify a novel eccentricity behavior, the innermost branch becomes increasingly circular with increasing energy or angular momentum, while outer branches exhibit greater eccentricity and a larger apastron-periastron separation. These features, absent in previous studies, are unique signatures of non-monotonic metric functions. In contrast, monotonic cases yield a single-well potential, a unique marginally bound orbit, and a single periodic orbit branch per $q$, consistent with earlier findings. Our results highlight the critical role of the metric function's shape in determining the orbital structure around dyonic black holes.

We analyze gravitational lensing, in particular the shadow and photon rings, in the Ernst spacetime, also known as the Schwarzschild-Melvin spacetime, which describes a Schwarzschild black hole immersed in a homogenous magnetic field. Although the geodesic equation in this spacetime is chaotic, there are some relevant features that can be determined analytically. Among other things, we give analytic formulas for the vertical diameter of the shadow for an observer at arbitrary inclination and for the horizontal diameter of the shadow for an observer in the equatorial plane. Moreover, we use the strong-deflection formalism for analytically calculating the so-called photon rings of order $\ge 2$ and we use the recently introduced gap parameter $\Delta _2$ for distinguishing lensing of an Ernst black hole from that of a Schwarzschild black hole.

TianQin is a proposed space-based gravitational wave detector mission that employs inter-satellite laser interferometry. Suppressing measurement noise and achieving high sensitivity require accurate alignment of multiple onboard interferometers after laser link acquisition. However, due to huge armlengths and varying point-ahead angles, the fine alignment of the transmitted beams can be particularly challenging, which needs to take into account both received laser power and far-field wavefront errors. To tackle this issue for TianQin which has small point-ahead angle variations, we propose an efficient alignment strategy that relies on finding the maximum-intensity direction of the transmitted beam as the alignment reference. The direction can be estimated through a quatrefoil scan of the local transmitted beam and the corresponding intensity measurement from the remote satellite. Under TianQin's fixed-value compensation of the point-ahead angles, simulation results reveal that the proposed strategy is capable of aligning the transmitted beams within 20 nrad from the mean value of the point-ahead angles, while the tilt-to-length coupling associated with far-field wavefront error can meet the requirement given a transmitted beam aberration of $\lambda/40$ RMS.

Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological simulations. While the so-called separate universe approach allows one to account for the effect of curvature on the expansion rate in small sub-volumes, the non-Euclidean geometry is harder to accommodate. It becomes important when observables are computed over large distances, e.g. when photons travel to us from high redshift. Here we present a fully relativistic framework to run cosmological simulations for curved spatial geometry. The issue of consistent boundary conditions is solved by embedding a spherical cap of the curved spacetime into a hole within a flat exterior, where it can undergo free expansion. The geometric nature of gravity is made explicit in our framework, allowing for a consistent forward modelling of observables inside the curved patch. Our methodology would also work with any Newtonian code to a good approximation, requiring changes only to the initial conditions and post-processing.

In this investigation, we present a singularity free interior solution of the Einstein field equation for a class of anisotropic compact objects in dimensions $D\geq4$. In accordance with the concept of Vaidya and Tikekar, the geometry of the physical $(D-1)$-space of a star corresponding to $t=constant$ hypersurface is assumed to be of a $(D-1)$ spheroid. For the fulfilment of causality condition, a limit of the spheroidal parameter ($\lambda$) is noted depending on the values of amount of anisotropy ($\alpha$) and space-time dimensions ($D$). We note that by switching off the extra parameters ($\alpha$ and $D$), previously obtained limit of $\lambda$ can be generated. To validate our findings, we compare the results obtained from our model with observational data of PSR J1614-2230 (mass=$1.908^{+0.016}_{-0.016}M_{\odot}$, radius=$11.93^{+0.50}_{-0.50}km$). It is noted that the best fit equation of state corresponds to polynomial equation of state of the order of five. We use this finding to develop a density dependent MIT bag model which seems to be useful for the correct description of compact object in our model. The mass radius relation shows that our model mimics a wide range of recently observed pulsars in four and higher dimensions. Furthermore, we also found that our model exhibits stability according to Generalised TOV equation, Herrera cracking condition, and the adiabatic index.

We study quantum corrections to the $\Lambda$CDM model model arising from a minimum measurable length in Heisenberg's uncertainty principle. We focus on a higher-order Generalized Uncertainty Principle, beyond the quadratic form. This generalized GUP introduces two free parameters, and we determine the modified Friedmann equation. This framework leads to a perturbative cosmological model that naturally reduces to $\Lambda$CDM in an appropriate limiting case of the deformation parameters. We construct the modified cosmological scenario, analyze its deviations from the standard case, and examine it as a mechanism for the description of dynamical dark energy. To constrain the model, we employ Cosmic Chronometers, the latest Baryon Acoustic Oscillations from the DESI DR2 release, and Supernova data from the PantheonPlus and Union3 catalogues. Our analysis indicates that the modified GUP model is statistically competitive with the $\Lambda$CDM scenario, providing comparable or even improved fits to some of the combined datasets. Moreover, the data constrain the deformation parameter of the GUP model, with the preferred value found to be negative, which corresponds to a phantom regime in the effective dynamical dark energy description.

We consider static spacetimes in spherical coordinates whose angular sector is described by a Finsler metric rather than the standard round metric on $S^2$. Our first contribution is kinematical: keeping the lapse and radial factors $e^{\nu(r)}$, $e^{\vartheta(r)}$ arbitrary and using only Killing symmetries and the null constraint, we derive model--independent relations for circular photon orbits and the effective dynamics. Specializing the Finsler metric to a positive constant flag curvature Randers sphere we derive exact expressions for the conserved angular charge and the critical impact parameter, and we quantify a Finslerian Sagnac--type effect. Our second contribution is dynamical: we consider the field equations used in the literature to fix $(e^{\nu},e^{\vartheta})$. We revisit the hairy black hole family in a recent paper by Nekouee et al. demonstrating that the equatorial restriction employed in such a work eliminates the genuinely Finslerian features and showing that the claimed new solutions reproduce previously known results obtained by Ovalle et al.

We present results from the search for an isotropic gravitational-wave background using Advanced LIGO and Advanced Virgo data from O1 through O4a, the first part of the fourth observing run. This background is the accumulated signal from unresolved sources throughout cosmic history and encodes information about the merger history of compact binaries throughout the Universe, as well as exotic physics and potentially primordial processes from the early cosmos. Our cross-correlation analysis reveals no statistically significant background signal, enabling us to constrain several theoretical scenarios. For compact binary coalescences which approximately follow a 2/3 power-law spectrum, we constrain the fractional energy density to $\Omega_{\rm GW}(25{\rm Hz})\leq 2.0\times 10^{-9}$ (95% cred.), a factor of 1.7 improvement over previous results. Scale-invariant backgrounds are constrained to $\Omega_{\rm GW}(25{\rm Hz})\leq 2.8\times 10^{-9}$, representing a 2.1x sensitivity gain. We also place new limits on gravity theories predicting non-standard polarization modes and confirm that terrestrial magnetic noise sources remain below detection threshold. Combining these spectral limits with population models for GWTC-4, the latest gravitational-wave event catalog, we find our constraints remain above predicted merger backgrounds but are approaching detectability. The joint analysis combining the background limits shown here with the GWTC-4 catalog enables improved inference of the binary black hole merger rate evolution across cosmic time. Employing GWTC-4 inference results and standard modeling choices, we estimate that the total background arising from compact binary coalescences is $\Omega_{\rm CBC}(25{\rm Hz})={0.9^{+1.1}_{-0.5}\times 10^{-9}}$ at 90% confidence, where the largest contribution is due to binary black holes only, $\Omega_{\rm BBH}(25{\rm Hz})=0.8^{+1.1}_{-0.5}\times 10^{-9}$.

The singularities present at the centre of black holes signal a break down of the classical theory. In this paper, we demonstrate a resolution of the Schwarzschild-(Anti-)de Sitter singularity by imposing unitary evolution with respect to unimodular time. Employing the Henneaux-Teitelboim formulation of unimodular gravity, we perform a canonical quantization on a symmetry-reduced Schwarzschild-(Anti-) de Sitter model. This leads to a Wheeler-DeWitt equation that effectively becomes a Schrödinger equation in unimodular time. By imposing unitarity, we discover a family of quantum theories in which the classical singularity is resolved. These theories each allow only semiclassical states corresponding to one mass sign: either positive, negative, or zero. Furthermore, we derive an analytical expression for the quantum-corrected Schwarzschild metric, which is modified by a new length scale $r_{min}$ that governs the black hole's transition to a white hole.

In this paper we obtain and study images of accretion disks around static spherically symmetric black holes in hybrid metric-Palatini gravity. Semi-analytic ray-tracing methods in curved spacetime are employed to generate the images of the disk for different scalar field configurations, including both Higgs-type potentials and cases without a potential. The resulting images, including both redshift and intensity maps, are analyzed. The results show that the scalar field parameters play a significant role in shaping both the direct and secondary images of the disk, while the inclination angle primarily affects the asymmetry and brightness distribution. In particular, configurations with extreme scalar field values lead to cooler and dimmer disk compared to General Relativity. Furthermore, the structure and angular size of the secondary ring exhibit noticeable deviations from General Relativity, offering a potential observational signature. Through direct comparison between hybrid metric-Palatini gravity and General Relativity images, we conclude that future high-resolution observations of black hole shadows could effectively distinguish this modified gravitational theory and constrain underlying scalar field parameters.

The scalar perturbations of thick braneworld models provide critical insights into their matter-geometry relationship, distinct from tensor modes. This work systematically investigates quasinormal modes and gravitational echoes from scalar perturbations in a thick brane model exhibiting internal structure and brane splitting. Using the WKB method, direct integration, and Bernstein spectral techniques, we compute quasinormal frequencies across different parameter regimes, addressing both single and double-barrier effective potentials. Time-domain evolution of wave packets reveals clear echo signals for split brane configurations ($s > 1, \delta > 1$), produced by successive reflections between sub-branes. A key finding is the position-dependence of echo modes within the extra dimension: observers located on a sub-brane detect clean periodic signals, whereas those situated between sub-branes observe more complex, modulated waveforms. This effect offers a distinct signature of the brane's internal structure. The observed echoes, along with consistent frequency- and time-domain results, advance the understanding of thick brane dynamics and open an observational window into warped extra dimensions. Moreover, the similarity between the effective potential in thick brane scenarios and those of black holes and wormholes offers valuable perspectives for studying echo-related phenomena in these gravitational systems.

A few years ago, Bemfica, Disconzi, Noronha, and Kovtun (BDNK) formulated the first causal, stable, strongly hyperbolic, and locally well-posed theory of first-order viscous relativistic hydrodynamics. Since their inception, there have been several numerical and analytic studies of the BDNK equations which have revealed their promise in modeling relativistic flows when viscous, first-order corrections to ideal hydrodynamics are important. In this paper, we present numerical solutions to the BDNK equations for a $4$D conformal fluid in Minkowski spacetime constrained to the surface of a geometric sphere. We numerically solve the underlying equations of motion by use of finite difference methods applied in cubed-sphere coordinates -- a multi-block grid structure which regularly and continuously covers the surface of a sphere. We present three test cases of our code: linearized fluid perturbations of equilibrium states, a smooth, stationary initial Gaussian pulse of energy density, and Kelvin-Helmholtz-unstable initial data. In the Gaussian test case with sufficiently large entropy-normalized shear viscosity, the flow, though initialized in equilibrium, dynamically diverges away from equilibrium and the regime of validity of first-order hydrodynamics as very steep gradients form in the solution, causing convergence to be lost in the numerical simulation. This behavior persists at all grid resolutions we have considered, and also occurs at much higher resolutions in simulations of planar-symmetric ($1+1$)D conformal flows. These solutions provide numerical evidence that singularities in solutions to the BDNK equations can form in finite time from smooth initial data. The numerical methods we employ on the two-sphere can be readily extended to include variations in the radial direction, allowing for full ($3+1$)D simulations of the BDNK equations in astrophysical applications.

In recent years, modifications to General Relativity (GR) have been explored to address cosmological observations, particularly in the context of late-time cosmic acceleration. Among these, modifications based on the Teleparallel Equivalent of General Relativity (TEGR), particularly $f(T)$ gravity, have gained significant attention. In this work, we investigate the scalar perturbations in $f(T)$ gravity, focusing on how these perturbations modify the Poisson and lensing equations and how they impact cosmological observables. By incorporating observational data from cosmic chromatometers, Big Bang nucleosynthesis, the DESI BAO survey, and Type Ia Supernovae (SNe Ia), we derive constraints on the parameters of the $f(T)$ power-law model. Our results suggest that $f(T)$ gravity can effectively alleviate some of the tensions observed in the standard $\Lambda$CDM model, including the Hubble constant ($H_0$) discrepancy. Furthermore, the evolution of the supernova luminosity and its dependence on the gravitational constant are considered to refine the measurement of cosmological parameters. The model's ability to address the $H_0$ tension is critically examined, and we find that $f(T)$ gravity offers a viable alternative to the standard model. The work concludes by comparing the fits of the $f(T)$ gravity model to the $\Lambda$CDM model using various information criteria, revealing key insights into the viability of modified gravity in contemporary cosmology.

Quasi-Periodic Eruptions (QPEs) are luminous, recurring X-ray outbursts from galactic nuclei, with timescales of hours to days. While their origin remains uncertain, leading models invoke accretion disk instabilities or the interaction of a massive black hole (MBH) with a lower-mass secondary in an extreme mass ratio inspiral (EMRI). EMRI scenarios offer a robust framework for interpreting QPEs by characterizing observational signatures associated with the secondary's orbital dynamics. This, in turn, enables extraction of the MBH/EMRI physical properties and provides a means to test the EMRI scenario, distinguishing models and addressing the question: what can QPE timings teach us about massive black holes and EMRIs? In this study, we employ analytic expressions for Kerr geodesics to efficiently resolve the trajectory of the secondary object and perform GPU-accelerated Bayesian inference to assess the information content of QPE timings. Using our inference framework, referred to as QPE-FIT (Fast Inference with Timing), we explore QPE timing constraints on astrophysical parameters, such as EMRI orbital parameters and MBH mass/spin. We find that mild-eccentricity EMRIs ($e\sim0.1-0.3$) can constrain MBH mass and EMRI semimajor axis/eccentricity to the 10% level within tens of orbital periods, while MBH spin is unconstrained for the explored semimajor axes $\geq 100R_g$ and monitoring baselines $\mathcal{O}(10-100\rm)$ orbits. Introducing a misaligned precessing disk generally degrades inference of EMRI orbital parameters, but can constrain disk precession properties within 10-50%. This work both highlights the prospect of QPE observations as dynamical probes of galactic nuclei and outlines the challenge of doing so in the multimodal parameter space of EMRI-disk collisions.

It was recently shown that a black hole (or any Killing horizon) will decohere any quantum superposition in their vicinity. I review three distinct but equivalent arguments that illustrate how this phenomenon arises: (1) entanglement with "degrees of freedom" in the interior (2) the absorption of soft, entangling radiation emitted by the superposition and (3) interactions with the quantum, fluctuating multipole moments of a black hole arising from ultra low frequency Hawking quanta. The relationship between "soft hair" and interactions with "internal degrees of freedom" is emphasized and some implications for the nature of horizons in a quantum theory of gravity are discussed.

Realising $F$-term slow-roll inflation in supergravity is non-trivial due to the well-known $\eta$-problem. The common strategy to solve the problem is to impose a shift symmetry on the Kähler potential, but this often leads to a negative potential in the large-field regime. To avoid negative potentials, an additional superfield called the stabiliser is usually added with a desired interaction. An alternative mechanism in supergravity, avoiding the use of a stabiliser superfield, was earlier proposed by two of us in the setup with a single chiral superfield having inflaton and goldstino amongst its field components. In this work, we extend that alternative mechanism to multi-superfield models of inflation, thereby providing a generic framework for embedding a wide class of single- and multi-field inflation models into supergravity. We illustrate our approach by several concrete examples of multi-field inflation and clarify the conditions required to avoid tachyonic instabilities during multi-field evolution. Our proposal significantly broadens the theoretical landscape of $F$-term inflation models in supergravity.

Neutron stars are the most compact horizonless objects in the Universe, exhibiting the strongest known magnetic fields. They are potential sources of coincident gravitational waves and electromagnetic radiation across the entire spectrum. However, the internal configuration of their magnetic fields and the mechanisms that stabilize them remain open questions. As a step forward in understanding the timescale for the emergence of magnetic instabilities that disrupt stellar field configurations, we study the impact of stellar rotation using three-dimensional general relativistic numerical simulations of uniformly rotating, isolated neutron stars threaded by strong, poloidal, pulsar-like magnetic fields. The initial stellar configurations assume perfect conductivity and are stationary and axisymmetric. We explore a range of angular velocities, from non-rotating stars to those near the mass-shedding limit. We find that the stars spontaneously develop differential rotation, which triggers the appearance of a strong toroidal magnetic field component. Non-rotating neutron stars are unstable to the Tayler and Parker instabilities, which significantly change the magnetic field geometry. These instabilities lead to a rapid reduction of the initial magnetic energy by $\sim 99\%$ within $\sim 4$ Alfvén times of their onset. In contrast, rotation significantly delays the development of these instabilities and, in some cases, mitigates their effects. Highly rotating models retain up to $\sim 30\%$ of their magnetic energy for at least $\sim 10$ Alfvén times. Our results suggest that rotation plays a crucial role in stabilizing the magnetic field of neutron stars, regardless of its initial configuration.

The Laser Interferometer Space Antenna (LISA) will observe mHz gravitational waves from a wide variety of astrophysical sources. Of these, some will be characterizable as individual deterministic signals; the remainder will overlap to create astrophysical confusion noise. These sources of confusion noise are known as stochastic gravitational wave backgrounds (SGWBs). LISA data is expected to include several such astrophysical SGWBs, including the notable Galactic binary foreground, SGWBs from white dwarf binary populations in satellite galaxies of the Milky Way, and the SGWB from extragalactic stellar-origin binary black holes far from merger. To characterize these astrophysical signals and attempt to seek out possible underlying backgrounds of cosmological origin, it will be necessary to separate the contribution of each SGWB from that of the others. Crucially, several of these SGWBs are expected to be highly anisotropic on the sky, providing a powerful tool for spectral separation. To this end, we present BLIP 2.0: a flexible, GPU-accelerated framework for simulation and Bayesian analysis of arbitrary combinations of isotropic and anisotropic SGWBs. We leverage these capabilities to demonstrate for the first time spectral separation of the Galactic foreground, the Large Magellanic Cloud SGWB, and the SGWB from extragalactic stellar-origin binaries, and show a proof-of-concept for placing upper limits on the detection of an underlying isotropic cosmological SGWB in the presence of multiple astrophysical foregrounds.

According to the Kibble-Zurek mechanism (KZM), the density of topological defects created during a second-order phase transition is determined by the correlation length at the freeze-out time. This suggests that the final configuration of topological defects in such a transition is largely established during the impulse regime, soon after the critical point is traversed. Motivated by this, we conjecture that machine learning (ML) can predict the final configuration of topological defects based on the time evolution of the order parameter over a short interval in the vicinity of the critical point, well before the order parameter settles into the emerging new minima resulting from spontaneous symmetry breaking. Furthermore, we show that the predictability of ML also follows the power law scaling dictated by KZM. We demonstrate these using a Recurrent Neural Network.

In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix defined on a single Cauchy surface. We present the construction of the spacetime density matrix in general quantum systems and its representation via the Schwinger Keldysh path integral. We further introduce a super-operator framework, within which the spacetime density matrix appears as a special case, and discuss possible generalizations from this perspective. We also show that the spacetime density matrix satisfies a Liouville von Neumann type equation of motion. When considering subsystems, a reduced spacetime density matrix can be defined by tracing over complementary degrees of freedom. We study the general properties of its moments and, in particular, derive universal short time behavior of the second moment. We find that coupling between subsystems plays a crucial role in obtaining nontrivial results. Assuming weak coupling, we develop a perturbative method to compute the moments systematically.

Detailed stellar evolution and supernova models yield a bimodal black-hole mass distribution with a narrow peak around 10 solar masses from stars within a narrow range of progenitor properties and a second broader peak starting around 20 solar masses from very massive progenitors. This bimodal black-hole mass distribution leads to a characteristic distribution of chirp masses of merging binary black holes, with two main peaks arising from the merger of two black holes where both come either from the low- or the high-mass peak and a smaller peak in between from the mixed merger of a low-mass and a high-mass black hole. We carry out a population synthesis study of binary black hole formation and compare the results to the observed chirp masses of gravitational-wave events. We find that only the bimodal black-hole mass prescription is able to reproduce the structure of peaks and gaps in the observed chirp-mass distribution, which is not matched by predictions from other remnant mass prescriptions in the literature.

We present a set of preliminary simulations of intermediate mass ratio inspirals (IMRIs) inside dark matter (DM) spikes accounting for post-Newtonian corrections the interaction between the two black holes up to the order 2.5 in $c^2$, as well as relativistic corrections to the dynamical friction (DF) force exerted by the DM distribution. We find that, incorporating relativity reduces of a factor $1/2$ the inspiral time, for equivalent initial orbital parameters, with respect to the purely classical estimates. Vice versa, neglecting the DF of the spike systematically yields longer inspiral times.

We address various cosmological phenomenologies in the symmetric teleparallel framework both in background and perturbation such as cosmic expansion, gravitational coupling constant, gravitational waves propagation. Focusing on logarithmic extensions of $f(Q)$ models, we performed Bayesian analysis using the most-recent cosmological data, DESI DR2, Pantheon+. We also utilized a compilation of redshift space distortions ($f \sigma_8$) dataset to constrain the growth of structures in each of the models modulated by the effective gravitational coupling. We find that our extended Logarithmic $f(Q)$ models are well-constrained by the current cosmological data and are able to describe the late-time cosmic acceleration. The inverse Logarithmic model we introduce is also able to accommodate a phantom-like dark energy equation of state at late times, which is consistent with the recent DESI DR2 observations. We report explicitly predictions for the effective gravitational coupling ($\mu$), and the amplitude damping parameter of gravitational wave ($\nu$) solely based on the background data, which can be tested against future observations. While the two Log-based extensions we have introduced here perform equivalently on the background level, they provide contrasting predictions for the evolution of effective Gravitational constant and propagation of gravitational waves, which should be constrained against the future perturbation data.

Numerical relativity waveforms are a critical resource in the quest to deepen our understanding of the dynamics of, and gravitational waves emitted from, merging binary systems. We present 181 new numerical relativity simulations as the second MAYA catalog of binary black hole waveforms (a sequel to the Georgia Tech waveform catalog). Most importantly, these include 55 high mass ratio (q >= 4), 48 precessing, and 92 eccentric (e > 0.01) simulations, including seven simulations which are both eccentric and precessing. With these significant additions, this new catalog fills in considerable gaps in existing public numerical relativity waveform catalogs. The waveforms presented in this catalog are shown to be convergent and are consistent with current gravitational wave models. They are available to the public at this https URL.

Space-based gravitational wave detectors such as TianQin, LISA, and TaiJi have the potential to outperform themselves through joint observation. To achieve this, it is desirable to practice joint data analysis in advance on simulated data that encodes the intrinsic correlation among the signals found in different detectors that operate simultaneously. In this paper, we introduce GWSpace, a package that can simulate the joint detection data from TianQin, LISA, and TaiJi. The software is not a groundbreaking work that starts from scratch. Rather, we use as many open-source resources as possible, tailoring them to the needs of simulating the multi-mission science data and putting everything into a ready-to-go and easy-to-use package. We shall describe the main components, the construction, and a few examples of application of the package. A common coordinate system, namely the Solar System Barycenter (SSB) coordinate system, is utilized to calculate spacecraft orbits for all three missions. The paper also provides a brief derivation of the detection process and outlines the general waveform of sources detectable by these detectors.

In the last decade, the first law of binary black hole mechanics played an important unifying role in the gravitational two-body problem. More recently, binary black hole scattering and the application of high-energy physics methods have provided a new avenue into this classical problem. In this Letter, we connect these two themes by extending the first law to the case of scattering orbits. We present derivations based on classical S-matrix, Hamiltonian, and pseudo-Hamiltonian methods, the last of which allows us to include dissipative effects for the first time. Finally, a "boundary to bound" map links this first law to the traditional bound-orbit version. Through this map a little-known observable for scatter orbits, the elapsed proper time, is mapped to the Detweiler redshift for bound orbits, which is an invariant building block in gravitational waveform models.

In tests of gravity using gravitational waves (GWs), GW events analyzed are often selected based on specific criteria, particularly the signal-to-noise ratio. However, such event selection can introduce bias into parameter estimation unless the selection effect is appropriately taken into account in the analysis. In this paper, we investigate how event selection with certain prior information affects parameter inference within the scalar-tensor polarization framework, focusing on the measurement of the scalar mode amplitude parameters. We find that for the Tensor+Scalar(dipole) model, the amplitude of the scalar dipole radiation is overestimated when its true value is nonzero while there is no false deviation in the absence of the scalar mode. The same bias is expected to occur also for the Tensor+Scalar(quadrupole) model. However, the error typically exceeds the bias as the scalar quadrupole mode is difficult to be distinguished from the tensor mode.

This study investigates the gravitational dynamics of a spherically symmetric black hole embedded within a dark matter halo, focusing on the impact of the dark matter halo on time-like particle geodesics. We analyze key orbital parameters, including marginally bound orbits, innermost stable circular orbits, and periodic orbits, demonstrating how the dark matter halo alters their energy and angular momentum compared to an isolated black hole. Furthermore, we calculate the gravitational waveforms emitted by these periodic orbits, providing potential observational signatures for such systems. Our results demonstrate a clear correlation between the gravitational waveforms emitted by a small object orbiting a supermassive black hole and the object's zoom-whirl orbital behavior. Higher zoom numbers correspond to more complex waveform substructures. The presence of a dark matter halo significantly impacts these waveforms. We have conducted a detailed analysis of the frequency spectra of the gravitational waveforms arising from these periodic orbits and evaluated their potential detectability. This research contributes to a deeper understanding of the interplay between black holes and dark matter halos, offering insights into their complex gravitational interactions.

Previous studies have identified potential instabilities in self-interacting vector theories associated with the breakdown of the well-posedness of the initial-value problem. However, these conclusions are restricted to Abelian vector fields, leaving room to explore alternative setups, such as non-Abelian vector fields with internal symmetries. Building on this idea, we study the well-posed 1+1 evolution of self-interacting SU(2) vector fields minimally coupled to gravity within the framework of the 't Hooft-Polyakov magnetic monopole configuration. In this context, we present a counterexample in which self-interacting vector fields retain a well-posed initial value problem formulation. Remarkably, this system exhibits the same characteristic speeds as those found in general relativity (GR) in one spatial dimension. Unlike its Abelian counterpart, we achieve stable numerical evolutions across a wide range of initial conditions within a fully non-linear dynamical background, as evidenced in our time integration algorithm. Although our conclusions are strictly valid for the spherical symmetry case with only magnetic part for the vector field, this study serves as a valuable diagnostic tool for investigating more realistic astrophysical scenarios in three-dimensional settings and under more general background and vector field configurations.

Semi-analytical waveform models for black hole binaries require calibration against numerical relativity waveforms to accurately represent the late inspiral and merger, where analytical approximations fail. After the fitting coefficients contained in the model are optimized, they are typically held fixed when the model is used to infer astrophysical parameters from real gravitational-wave data. Though point estimates for the fitting parameters are adequate for most applications, they provide an incomplete description of the fit, as they do not account for either the quality of the fit or the intrinsic uncertainties in the numerical relativity data. Using the IMRPhenomD model, we illustrate how to propagate these uncertainties into the inference by sampling the fitting coefficients from a prior distribution and marginalizing over them. The prior distribution is constructed by ensuring that the model is compatible with a training set of numerical relativity surrogates, within a predefined mismatch threshold. This approach demonstrates a pathway to mitigate systematic bias in high signal-to-noise events, particularly when envisioned for the next generation of semi-analytical models.

We perform the shadow radius analysis of a charged Horndeski black hole (CHB) and the naked singularity (NS) with secondary scalar hair obtained from the Einstein-Horndeski-Maxwell theory. For this analysis, we include the beyond Horndeski black hole (bH) with secondary scalar hair and the magnetically charged black hole (MC) found from the Einstein-Euler-Heisenberg theory. It is worth noting that the NS versions of CHB and bH arise from the charge extension of their photon spheres, while there is no NS version for MC. One branch (i) from the CHB is a point in the horizon realization but it shows up on the photon sphere and shadow radius. The shadow radius for the CHB is the nearly same as that for the MC with a single horizon and the charge of the NS is constrained by the EHT observation. From classical scattering analysis, it turns out that i-NS and NS play different roles from CHB, bH, and MC.

We obtain the generalized quasi-Keplerian parametrization for compact binaries on quasihyperbolic orbits at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories, extending the analogous results for quasielliptic systems arXiv:2401:06844. In particular, we compute the conservative scattering angle and impact parameter at 2PN. Our results are consistent with the 2PN conservative scatter-to-bound map in these theories between the scattering angle and the periastron advance. We then compute the total energy and angular momentum lost by the system and study the limiting cases of parabolic orbits and bremsstrahlung, including a re-expansion of our results at seventh post-Minkowskian order. Flux-balance arguments then allow us to compute the dissipative contributions to the scattering angle at 1.5PN and 2.5PN, completing the full scattering angle at 2.5PN in these theories. Finally, we obtain, in general relativity, an expression for the 3PN impact parameter in the conservative sector, correcting previous literature.

This paper develops a renormalized perturbation theory framework for nonlinear structure formation in a broad class of modified gravity models that exhibit Vainshtein screening, with a focus on a viable subclass of Horndeski theories. We extend earlier perturbative methods, originally applied to DGP model, to construct a self-consistent treatment that captures both the linear modifications to gravity at large scales and the nonlinear screening effects at small scales. In the framework, the response of the gravitational potential to matter density fluctuations is characterized by renormalized propagators, leading to the definition of a nonlinear (or renormalized) effective gravitational constant. The paper details several numerical strategies to compute this renormalized gravitational constant. Numerical examples illustrate how the effective gravitational constant evolves with scale and redshift. These results are key to accurately predicting cosmological observables such as the matter power spectrum and bispectrum in modified gravity scenarios.

We study the class of six-dimensional $\Lambda$-vacuum spacetimes which admit a non-degenerate multiple Weyl aligned null direction l (thus being of Weyl type~II or more special) with a ``generic'' optical matrix. Subject to an additional assumption on the asymptotic fall-off of the Weyl tensor, we obtain the most general metric of this class, which is specified by one discrete (normalized) and three continuous parameters. All solutions turn out to be Kerr--Schild spacetimes of type~D and, in passing, we comment on their Kerr--Schild double copy. We further show that the obtained family is locally isometric to the general doubly-spinning Kerr-NUT-(A)dS metric with the NUTs parameters switched off. In particular, the Kerr-(A)dS subclass and its extensions (i.e., analytic continuation and ``infinite-rotation'' limit) are recovered when certain polynomial metric functions are assumed to be fully factorized. As a side result, a unified metric form which encompasses all three branches of the extended Kerr-(A)dS family in all even dimensions is presented in an appendix.

In this paper, the dynamical behavior of the accelerated expansion of the universe is discussed within the framework of $f(T)$ gravity, considering power law functional form of $ f(T)=\alpha (-T)^{n}$. Two distinct redshift-dependent parameterization of the deceleration parameter such as $q(z)=q_{0}+ q_{1}\left(\frac{ \ln(N+z)}{z+1}-\ln N \right)$ and $ q(z)=\frac{1}{2}+ \frac{q_{1}z+ q_{2}}{(1+z)^2} $ are considered. We have derived the Hubble parameter in terms of redshift and discussed its effect on other cosmological parameters. Using Bayesian statistical analysis and $\chi^2$-minimization, the median values of the model parameters for both the cosmic chronometer(CC) and the joint(CC + Pantheon) dataset have been determined. Further, energy density, pressure, the equation of state for Dark Energy, Energy condition and statefinder diagnostics are analyzed. The current age of the universe is also computed for these models.

We model a single black hole in equilibrium with a dark photon-cold dark matter environment. Representing the dark photon as a Proca field, we show that a Schwarzschild black hole grows vector-field "hair" when allowed to accrete from an infinite homogeneous bath of particles far from the horizon. We solve the Proca equation in linear perturbation theory, separating it using the vector spherical harmonics and Frolov-Krtouš-Kubizňák-Santos approaches for the odd-parity and even-parity sectors, respectively. In the "particle" dark matter regime, the field is purely infalling and exhibits a sharply peaked density profile, in concordance with the particle dark matter "spikes" studied in the literature. In the "wave" regime, the field exhibits standing waves, and the profile is smeared. We find a dark-matter density amplification upward of $10^7$ near the horizon. Though small for most black holes, we find the mass enclosed in the cloud can reach $\sim 1 \%$ of the black hole mass for large supermassive black holes. These black holes are also most susceptible to vector dark matter accretion, with mass accretion rates as large as $10 M_\odot/$yr.

This work presents a new black hole solution within the framework of a non-commutative gauge theory applied to Kalb-Ramond gravity. Using the method recently proposed in the literature [Nucl.Phys.B 1017 (2025) 116950], we employ the Moyal twist $\partial_r \wedge \partial_\theta$ to implement non-commutativity, being encoded by parameter $\Theta$. We begin by verifying that the resulting black hole no longer possesses spherical symmetry, while the event horizon remains unaffected by non-commutative corrections. The Kretschmann scalar is computed to assess the corresponding regularity. It turns out that the solution is regular, provided that the Christoffel symbols and related quantities are not expanded to second order in $\Theta$. We derive the thermodynamic quantities, including the Hawking temperature $T^{(\Theta,\ell)}$, entropy $S^{(\Theta,\ell)}$, and heat capacity $C_V^{(\Theta,\ell)}$. The remnant mass $M_{\text{rem}}$ is estimated by imposing $T^{(\Theta,\ell)} \to 0$, although the absence of a physical remnant indicates complete evaporation. Quantum radiation for bosons and fermions is analyzed via the tunneling method, where divergent integrals are treated using the residue theorem. Notably, in the low-frequency regime, the particle number density for bosons surpasses that of fermions (at least within the scope of the methods considered here). The effective potential for a massless scalar field is obtained perturbatively, enabling the computation of quasinormal modes and the time-domain profiles. Finally, further bounds on $\Theta$ and $\ell$ (Lorentz-violating paramter) are derived from solar system tests, including the perihelion precession of Mercury, light deflection, and the Shapiro time delay.

Improving a singularity theorem in General Relativity by Galloway and Ling we show the following (cf.\ Theorem 1): If a globally hyperbolic spacetime $M$ satisfying the null energy condition contains a closed, spacelike Cauchy surface $(V,g,K)$ (with metric $g$ and extrinsic curvature $K$) which is 2-convex (meaning that the sum of the lowest two eigenvalues of $K$ is non-negative), then either $M$ is past null geodesically incomplete, or $V$ is a spherical space, or $V$ or some finite cover is a surface bundle over the circle, with totally geodesic fibers. Moreover, (cf.\ Theorem 2) if $(V,g,K)$ admits a $U(1)$ isometry group with corresponding Killing vector $\xi$, we can relax the convexity requirement in terms of a decomposition of $K$ with respect to the directions parallel and orthogonal to $\xi$. Finally, (cf. Propositions 1-3) in the special cases that $V$ is either non-orientable, or non-prime, or an orientable Haken manifold with vanishing second homology, we obtain stronger statements in both Theorems without passing to covers.

We show that the arrow of time is intimately related to the geometry and topology of the whole universe, and is therefore best understood as a cosmological phenomenon.

We present a theoretical investigation of black hole solutions in Kalb-Ramond gravity embedded with quintessence fields. Our study examines how combined effects of Lorentz violation through the Kalb-Ramond field parameter $\eta$ and exotic matter contributions via quintessence parameters $(\mathrm{C}, w)$ systematically modify spacetime geometry, particle dynamics, and observational signatures compared to standard Schwarzschild black holes. The analysis encompasses geodesic motion for both photons and massive particles, revealing substantial modifications to effective potentials, photon sphere characteristics, and innermost stable circular orbit properties. We derive analytical expressions for black hole shadow radii across different quintessence states, demonstrating systematic parameter dependencies enabling observational discrimination between theoretical frameworks. Our perturbation analysis of scalar and electromagnetic fields shows how Lorentz violation and quintessence effects alter wave propagation and stability properties. Using Gauss-Bonnet theorem methodology, we calculate gravitational lensing deflection angles incorporating both modified gravity and exotic matter contributions. The thermodynamic investigation reveals complex phase structures with modified Hawking temperature evolution, Gibbs free energy characteristics, and specific heat capacity behavior significantly deviating from general relativity predictions. Lorentz violation amplifies gravitational effects, whereas quintessence exerts counteractive forces, generating complex parameter spaces allowing precise manipulation of observable quantiti

We recast the finite-region analysis of Einstein's equations that underpins the ER=EPR program into the loop quantum gravity (LQG) framework. By translating curvature-energy uncertainty relations into holonomy-flux kinematics, and by identifying Planckian Einstein-Rosen throats with single-puncture cuts through spin networks, we obtain a precise dictionary between entanglement and quantum geometry. Within this dictionary we derive the Barbero-Immirzi parameter directly from the entanglement/area increment of a minimal bridge, and show that a boundary edge-mode construction renders the Bekenstein - Hawking entropy coefficient universal and independent of $\gamma$ under a natural complex polarization. We further establish a refinement renormalization flow for spin-foam amplitudes driven by the finite-region curvature energy bound, which suppresses bubble divergences and yields a regulator-independent continuum limit under explicit conditions. Finally, we indicate observational consequences that follow from an $N$-party generalized uncertainty relation.

We consider the impact of the first string corrections of minimally coupled single scalar field theory on inflationary dynamics. Specifically we consider separately the string corrections $\sim \alpha'\xi(\phi)c_2\,\left( \partial_{\mu}\phi \partial^{\mu}\phi\right)^2$ and $\sim \alpha'c \square \phi \partial_{\mu}\phi \partial^{\mu}\phi$, where $\alpha'$ is the square of the string scale. Our aim is to develop a theory which is self consistent in the sense that the field equations reproduce themselves in the slow-roll approximation. Such a requirement for the theory with $\sim \alpha'\xi(\phi) c_2\left( \partial_{\mu}\phi \partial^{\mu}\phi\right)^2$ resulted to a trivial non-minimal coupling function $\xi(\phi)$, however a self-consistent framework emerged from the theory with correction term $\sim \alpha' c \square \phi \partial_{\mu}\phi \partial^{\mu}\phi$. The resulting theory can easily be worked out analytically and we obtained an inflationary theory that can easily be fitted with the Atacama Cosmology Telescope constraints on the scalar spectral index and the updated Planck constraints on the tensor-to-scalar ratio.

We show that the existence of massive neutron stars and asymptotic freedom of QCD place robust upper bounds on the lowest sound speed of the ultra-dense matter unattainable in neutron stars. Centered on worst-case scenarios, our limits are the most conservative among physical equations of state in the density range $\sim 2-40 n_0$. Discovery of $\gtrsim 2.6 M_\odot$ neutron stars, in combination with current multimessenger astrophysical constraints on the equation of state, would strongly support first-order phase transitions at high baryon densities.

The nature of one-loop corrections to long-wavelength CMB-scale modes in single-field inflation models with an intermediate USR phase remains a subject of active debate. In this work, we perform a detailed investigation into the regularization and renormalization of these one-loop corrections to the curvature perturbation power spectrum. Employing a combined UV-IR regularization scheme within the in-in formalism, we compute the regularized one-loop contributions, including those from the tadpole diagram, arising from both the cubic and quartic interaction Hamiltonians. We demonstrate that the fully regularized and renormalized fractional loop correction to the power spectrum is controlled by its peak value at the end of the USR phase, scaling as $\mathcal{P}_\mathrm{peak} \sim e^{6 \Delta N}$, where $\Delta N$ is the duration of the USR phase. This result confirms the original conclusion that loop corrections can become non-perturbatively large if the transition from the USR phase to the final slow-roll phase is instantaneous and sharp, potentially challenging the validity of such inflationary scenarios for primordial black hole formation.

We explore the correspondence between the parallel surfaces framework, and the minimal surfaces framework, to uncover and apply new aspects of the geometrical and mechanical content behind the so-called Lovelock-type brane gravity (LBG). We show how this type of brane gravity emerges naturally from a Dirac-Nambu-Goto (DNG) action functional built up from the volume element associated with a world volume shifted a distance $\alpha$ along the normal vector of a germinal world volume, and provide all known geometric structures for such a theory. Our development highlights the dependence of the geometry for the displaced world volume on the fundamental forms, as well as on certain conserved tensors, defined on the outset world volume. Based on this, LBG represents a natural and elegant generalization of the DNG theory to higher dimensions. Moreover, our development allows for exploring disformal transformations in Lovelock brane gravity and analyzing their relations with scalar-tensor theories defined on the brane trajectory. Likewise, this geometrical correspondence would enable us to establish contact with tractable Hamiltonian approximations for this brane gravity theory, by exploiting the linkage with a DNG model, and thus start building a suitable quantum version.

Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here, we show in Maxwell theory that there is an arguably more interesting relationship between the asymptotic symmetries and their charges, on one hand, and their finite-distance counterparts, on the other, without the need of a limit. Key to this observation is to embed the finite region in the global spacetime and identify edge modes as dynamical $\rm{U}(1)$-reference frames for dressing subregion variables. Distinguishing intrinsic and extrinsic frames, according to whether they are built from field content in- or outside the region, we find that non-trivial corner symmetries arise only for extrinsic frames. Further, the asymptotic-to-finite relation requires asymptotically charged ones (like Wilson lines). Such frames, called soft edges, extend to asymptotia and, in fact, realize the corner charge algebra in multiple ways, for example, by "pulling in" the asymptotic one from infinity, or physically through the addition of asymptotic soft and hard radiation. Realizing an infinite-dimensional algebra requires a new set of soft boundary conditions, relying on the distinction between extrinsic and intrinsic data. We identify the subregion Goldstone mode as the relational observable between extrinsic and intrinsic frames and clarify the meaning of vacuum degeneracy. We also connect the asymptotic memory effect with a more operational quasi-local one. A main conclusion is that the relationship between asymptotia and finite distance is frame-dependent; each choice of soft edge mode probes distinct cross-boundary data of the global theory.

(Abridged) Neutron stars (NSs), the densest known objects composed of matter, provide a unique laboratory to probe whether strange quark matter is the true ground state of matter. We investigate the parameter space of the equation of state of strange stars using a quantum chromodynamics (QCD)-informed model. The parameters - related to the energy density difference between quark matter and the QCD vacuum, the strength of strong interactions, and the gap parameter for color superconductivity - are sampled via quasi-random Latin hypercube sampling to ensure uniform coverage. To constrain them, we incorporate observational data on the maximum mass of NSs (from binary and merger systems), the radii of $1.4$ M$_{\odot}$ NSs (from gravitational wave and electromagnetic observations), and tidal deformabilities (from GW170817). Our results show that quark strong interactions play a key role, requiring at least a $20\%$ deviation from the free-quark limit. We also find that color superconductivity is relevant, with the gap parameter reaching up to $\sim 230$ MeV for a strange quark mass of $100$ MeV. The surface-to-vacuum energy density jump lies in the range $(1.1-2.2)$ $\rho_{\rm{sat}}$, where $\rho_{\rm{sat}} \simeq 2.7 \times 10^{14}$ g cm$^{-3}$. Observational constraints also imply that a $1.4$ M$_{\odot}$ quark star has a radius of $(10.0-12.3)$ km and tidal deformability between $270$ and $970$. These are consistent with the low mass and radius inferred for the compact object XMMU J173203.3-344518. Our results provide useful inputs for future studies on quark and hybrid stars, including their tidal properties, thermal evolution, quasi-normal modes, and ellipticities.

We study classical wormhole solutions in 3D gravity with end-of-the-world (EOW) branes, conical defects, kinks, and punctures. These solutions compute statistical averages of an ensemble of boundary conformal field theories (BCFTs) related to universal asymptotics of OPE data extracted from the 2D conformal bootstrap. Conical defects connect BCFT bulk operators; branes join BCFT boundary intervals with identical boundary conditions; kinks (1D defects along branes) link BCFT boundary operators; and punctures (0D defects) are endpoints where conical defects terminate on branes. We provide evidence for a correspondence between the gravity theory and the ensemble. In particular, the agreement of the $g$-function dependence results from an underlying topological aspect of the on-shell EOW brane action, from which a BCFT analogue of the Schlenker-Witten theorem also follows.

We explore asymptotically locally anti-de Sitter spacetimes exhibiting gravitational radiative behavior, employing null gauges that allow for a well-defined flat limit. The radiative content in the bulk is captured by the boundary Cotton and stress tensor, which we collect into a radiative vector. We reinterpret this vector holographically in terms of fluid variables in the dual boundary theory. For algebraically special solutions, we uncover a close connection between bulk radiation and dissipative corrections in the boundary stress tensor, demonstrating a direct link between radiation and entropy production in the boundary fluid. This reveals a rich interplay between radiative dynamics in the bulk and out-of-equilibrium conformal physics at the boundary. We then investigate the flat limit of this correspondence in the context of flat-space holography. In this setting, we construct a Carrollian analogue of the radiative vector and introduce Celestial observables, such as energy detectors, which emerge naturally from the bulk's radiative structure. Our analysis shows that bulk radiation sources the Carrollian viscous stress tensor and heat current, which encodes the Bondi news in this framework. We illustrate our results with explicit examples, including Robinson-Trautman spacetimes and accelerating black holes.