General relativity contains 16 variables in the framework of ADM-Vielbein formalism which are 6 more than metric formalism. These variables emerge due to additional symmetry of Local Lorentz Transformations. In the framework of the Hamiltonian approach, it is expected to find first class constraints which generate this gauge symmetry. We introduce the complete form of such constraints and show that they exactly obey the algebra of the Lorentz group.

We present a classical theory of gravity, which is singularity free at short distances and reduces to General Relativity at large distances. We discuss its implications.

This paper links the advanced formulation of the Generalized Uncertainty Principle, termed the Asymptotic Generalized Extended Uncertainty Principle (AGEUP), to the corpuscular framework to derive the AGEUP-inspired black hole metric. The former incorporates spacetime curvature effects to explore black hole dynamics under quantum gravitational corrections, while the latter is a view that black holes are Bose-Einstein condensates of weakly interacting gravitons. In a particular case, the phenomenological union between the AGEUP with cosmological constant $\Lambda$ to the corpuscular framework enabled a black hole metric that has a scaled mass, which depends on $\Lambda$ and the Planck length $l_{\rm Pl}$. Interesting implications occur, such as the maximum limit for mass $M$ where $\Lambda$ ceases to influence the black hole. Another is the derived value of the modulation factor of the EUP term, $\alpha$, if the large-scale fundamental length is defined solely as the cosmological horizon. Additional analysis were done through the shadow and deflection angle phenomena, deriving constraints on the quantum gravity modulation parameter $\beta$. Constraints from the Event Horizon Telescope (EHT) and Very Long Baseline Interferometry (VLBI) are discussed as avenues for verifying AGEUP-related deviations in black hole shadow radius and deflection angles, offering potential observational evidence of quantum gravitational effects at astrophysical scales. The findings suggest that AGEUP could be instrumental in providing hints on the quantum gravity nature of black holes, particularly in high-energy astrophysical contexts. By linking local black hole physics with large-scale curvature effects, AGEUP paves the way for further research at the intersection of quantum gravity and cosmology, with implications for observational astrophysics and the fundamental structure of spacetime.

Ultralight bosons are a hypothetical class of particles predicted under various extensions of Standard Model physics. As a result of the superradiance mechanism, we expect ultralight bosons, should they exist in certain mass ranges, to form macroscopic clouds around rotating black holes, so that we can probe their existence by looking for the long-transient gravitational wave emission produced by such clouds. In this paper, we propose a statistically robust framework for constraining the existence of ultralight vector bosons in the absence of detecting such a signal from searches targeting merger remnant black holes, effectively marginalizing over the uncertainties present in the properties of the target black holes. We also determine the impact of weak kinetic mixing with the ordinary photon and vector mass generation through a hidden Higgs mechanism on the constraining power of these searches. We find that individual follow-up searches, particularly with the next-generation gravitational wave detectors, can probe regions of parameter space for such models where robust constraints are still lacking.

It has been almost 40 years since the proposal of the idea that Hawking radiation of black holes does not lead to a complete evaporation but rather a "remnant" state. Though traditionally viewed with great criticisms especially from the high energy physics community, in recent years, various approaches have demonstrated that black hole remnants remain a viable possibility. In this review, which is primarily aimed as an introduction to the subject, we will discuss some possible routes to forming remnants and their respective properties and challenges.

In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations: Einstein--Gauss--Bonnet as well as cubic Lovelock gravities with vacuum, cosmological constant, perfect fluid, spatial curvature, and some of their combinations. Our analysis suggests that it is possible to set constraints on the parameters of the above-mentioned models from the simple requirement of the existence of a smooth transition from the initial singularity to a realistic low-energy regime. Initially, anisotropic space naturally evolves into a configuration with two isotropic subspaces, and if one of these subspaces is three-dimensional and is expanding while another is contracting, we call it realistic compactification. Of course, the process is not devoid of obstacles, and in our paper, we review the results of the compactification occurrence investigation for the above-mentioned models. In particular, for vacuum and $\Lambda$-term EGB models, compactification is not suppressed (but is not the only possible outcome either) if the number of extra dimensions is $D \geqslant 2$; for vacuum cubic Lovelock gravities it is always present (however, cubic Lovelock gravity is defined only for $D \geqslant 3$ number of extra dimensions); for the EGB model with perfect fluid it is present for $D=2$ (we have not considered this model in higher dimensions yet), and in the presence of spatial curvature, the realistic stabilization of extra dimensions is always present (however, such a model is well-defined only in $D \geqslant 4$ number of extra dimensions).

We introduce two new static, spherically symmetric regular black hole solutions that can be obtained from non-linear electrodynamics models. For each solution, we investigate the dynamic stability with respect to arbitrary linear fluctuations of the metric and electromagnetic field, and also examine the energy conditions that those black holes satisfy. Moreover, based on those solutions, we present two additional ones that satisfy the Limiting Curvature Condition. Finally, we make a comparison between the two solutions exploring their null geodesics and circular photon orbits.

We obtain a class of solutions corresponding to a generalization of the Hayward black hole by solving the Einstein equations coupled to a particular nonlinear electromagnetic field. The generalization is realized by considering, additionally, the presence of the cosmological constant and a source corresponding to an anisotropic fluid, namely, a fluid of strings, that surrounds the black hole. We show that the obtained class of solutions preserves or does not the regularity of the original Hayward black hole solution, depending on the values of the parameter $\beta$ which labels the different solutions. We discuss the characteristics of the solutions, from the point of view of the singularities of spacetime, by examining the behavior of the Kretschmann scalar as well as of the geodesics concerning their completeness. We analyze some aspects of thermodynamics, particularizing one of the solutions obtained, namely, for $\beta =-1/2$, in which case the regularity of the Hayward black hole is preserved. Some thermodynamic quantities are obtained and analyzed, for example, pressure, heat capacity, and the critical points, and we show how these quantities change for different values of the parameter $q$ associated with the original Hayward solution, as well as with the parameter $b$ associated with the presence of the fluid of strings. The phase transitions are also analyzed by using the equation of state and the Gibbs free energy.

Gravitational lensing of gravitational waves (GWs) provides a unique opportunity to study cosmology and astrophysics at multiple scales. Detecting microlensing signatures, in particular, requires efficient parameter estimation methods due to the high computational cost of traditional Bayesian inference. In this paper we explore the use of deep learning, namely Conditional Variational Autoencoders (CVAE), to estimate parameters of microlensed binary black hole (simulated) waveforms. We find that our CVAE model yields accurate parameter estimation and significant computational savings compared to Bayesian methods such as bilby (up to five orders of magnitude faster inferences). Moreover, the incorporation of CVAE-generated priors in bilby reduces the average runtime of the latter in about 48% with no penalty on its accuracy. Our results suggest that a CVAE model is a promising tool for future low-latency searches of lensed signals. Further applications to actual signals and integration with advanced pipelines could help extend the capabilities of GW observatories in detecting microlensing events.

In this work, we investigate static and spherically symmetric black hole solutions in $f(R,T)$ gravity, where $R$ is the curvature scalar and $T$ is the trace of the energy-momentum tensor, coupled to nonlinear electrodynamics (NLED). To construct our solutions, we adopt a linear functional form, $f(R,T) = R + \beta T$. In the limit $\beta = 0$, the theory reduces to General Relativity (GR), recovering $f(R,T) \approx R$. We propose a power-law Lagrangian of the form $\mathcal{L} = f_0 + F + \alpha F^p$, where $\alpha =f_0= 0$ corresponds to the linear electrodynamics case. Using this setup, we derive the metric functions and determine an effective cosmological constant. Our analysis focuses on specific cases with $p = 2$, $p = 4$, and $p = 6$, where we formulate analytic expressions for the matter fields supporting these solutions in terms of the Lagrangian as a function of $F$. Additionally, we verify the regularity of the solutions and study the structure of the event horizons. Furthermore, we examine a more specific scenario by determining the free forms of the first and second derivatives $\mathcal{L}_F(r)$ and $\mathcal{L}_{FF}(r)$ of the Lagrangean of the nonlinear electromagnetic field. From these relations, we derive the general form of $\mathcal{L}_{\text{NLED}}(r)$ using consistency relations. This Lagrangian exhibits an intrinsic nonlinearity due to the influence of two constants, $\alpha$ and $\beta$. Specifically, $\alpha$ originates from the power-law term in the proposed Lagrangian, while $\beta$ arises from the assumed linear function $f(R,T)$. The interplay of these constants ensures that the nonlinearity of the Lagrangian is governed by both $\alpha$ and $\beta$, rather than $\alpha$ alone.

While grey-body factors for a test scalar field in stringy black holes described by the renowned Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) solution have been analyzed in the literature, no such analysis exists for gravitons, likely due to the complexity of the perturbation equations. In this study, we utilize known data on quasinormal modes and the relationship between quasinormal modes and grey-body factors to derive these factors for gravitational and electromagnetic perturbations of the dilaton black hole. Our findings indicate that grey-body factors are significantly suppressed by the dilaton parameter as the black hole's charge approaches its extreme value. The iso-spectrality between axial and polar channels of perturbations is broken in the presence of the dilaton field, which leads to different grey-body factors for different types of perturbations.

We give a definitive characterization of the instability of the pressureless ($p=0$) critical ($k=0$) Friedmann spacetime to smooth radial perturbations. We use this to characterize the global accelerations away from $k\leq0$ Friedmann spacetimes induced by the instability in the underdense case. The analysis begins by incorporating the Friedmann spacetimes into a mathematical analysis of smooth spherically symmetric solutions of the Einstein field equations expressed in self-similar coordinates $(t,\xi)$ with $\xi=\frac{r}{t}<1$, conceived to realize the critical Friedmann spacetime as an unstable saddle rest point $SM$. We identify a new maximal asymptotically stable family $\mathcal{F}$ of smooth outwardly expanding solutions which globally characterize the evolution of underdense perturbations. Solutions in $\mathcal{F}$ align with a $k<0$ Friedmann spacetime at early times, generically introduce accelerations away from $k<0$ Friedmann spacetimes at intermediate times and then decay back to the same $k<0$ Friedmann spacetime as $t\to\infty$ uniformly at each fixed radius $r>0$. We propose $\mathcal{F}$ as the maximal asymptotically stable family of solutions into which generic underdense perturbations of the unstable critical Friedmann spacetime will evolve and naturally admit accelerations away from Friedmann spacetimes within the dynamics of solutions of Einstein's original field equations, that is, without recourse to a cosmological constant or dark energy.

Perturbative Quantum Chromodynamics corrections and the colour superconductivity indicate that strongly interacting matter can manifest unique physical behaviours under extreme conditions. Motivated by this notion, we investigate the interior structure and properties of quark stars composed of interacting quark matter, which provides a comprehensive avenue to explore the strong interaction effects, within the framework of $f(Q)$ gravity. A unified equation of state is formulated to describe various phases of quark matter, including up-down quark matter $(2SC)$, strange quark matter $(2SC+s)$, and the Colour-Flavor Locked $(CFL)$ phase. By employing a systematic reparametrisation and rescaling, the number of degrees of freedom in the equation of state is significantly reduced. Utilising the Buchdahl-I metric ansatz and a linear $f(Q)$ functional form, $f(Q)=\alpha_{0}+\alpha_{1}Q$, we derive the exact solutions of the Einstein field equations in presence of the unified interacting quark matter equation of state. For the $2SC$ phase, we examine the properties of quark stars composed of up-down quark matter. For the $(2SC+s)$and $CFL$ phases, we incorporate the effects of a finite strange quark mass $(m_{s}\neq0)$. The Tolman-Oppenheimer-Volkoff equations are numerically solved to determine the maximum mass-radius relations for each phase. Our results indicate that the model satisfies key physical criteria, including causality, energy conditions, and stability requirements, ensuring the viability of the configurations. Furthermore, the predicted radii for certain compact star candidates align well with observational data. The study highlights that quark stars composed of interacting quark matter within the $f(Q)$ gravity framework provide a robust and physically consistent stellar model across all considered phases.

In this paper, we study time-like geodesics around a spherically symmetric black hole in Kalb-Ramond (KR) gravity, characterized by the parameter $l$, which induces spontaneous Lorentz symmetry breaking. The geodesic equations and effective potential are derived to investigate the influence of $l$. We calculate the marginally bound orbits and innermost stable circular orbits, analyzing the parameter's impact. Periodic orbits are computed numerically and classified within the standard taxonomy, revealing significant effects of $l$ on their momentum and energy. Additionally, we explore an extreme mass ratio inspiral system under the adiabatic approximation to derive gravitational waveforms emitted by an object orbiting a supermassive black hole in KR gravity. These waveforms reflect the distinctive characteristics of periodic orbits and highlight the influence of $l$. With advancements in gravitational wave detection, these results offer insights into black holes influenced by Lorentz symmetry-breaking fields.

In the typical data analysis and waveform modelling of the gravitational waves (GWs) signals for binary black holes (BBHs), it's assumed to be isolate sources in the vacuum within the theory of general relativity (GR). However, various kinds of matters may exist around the source or on the path to the detector, and there also exist many different kinds of modified theories of gravity. The effects of these modifications can be characterized within the parameterized post-Einstein (ppE) framework, and the corresponding phase corrections on the waveform at leading post-Newtonian (PN) order are also expressed by the additional parameters for these effects. In this work, we consider the varying-G theory and the dynamical friction of the dark matter spike as an example. Both of these two effects will modify the waveform at -4PN order, if we choose the suitable power law index for the spike. We choose to use a statistic to characterize the dispersion between the posterior of $\dot G$ for different events. For different astronomical models, we find that this statistic can distinguish these two models very effectively. This result indicates that we could use this statistic to distinguish other degenerate effects with the detection of multiple sources.

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework" and provides a new perspective for understanding the Hawking effect of the black hole.

Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators should have employed adaptive time steps in principle, but they are often difficult in practical implementations. In fact, they work well if time transformation functions cause the time-transformed Hamiltonians to have the desired splits and approach 1 or constants for sufficiently large distances. However, they do not satisfy the requirement of step-size selections in this case. Based on the step-size control technique proposed by Preto $\&$ Saha, the nonadaptive time step time-transformed explicit symplectic methods are slightly adjusted as adaptive ones. The adaptive methods have only two additional steps and a negligible increase in computational cost as compared with the nonadaptive ones. Their implementation is simple. Several dynamical simulations of particles and photons near black holes have demonstrated that the adaptive methods typically improve the efficiency of the nonadaptive methods. Because of the desirable property, the new adaptive methods are applied to investigate the chaotic dynamics of particles and photons outside the horizon in a Schwarzschild-Melvin spacetime. The new methods are widely applicable to all curved spacetimes corresponding to Hamiltonians or time-transformed Hamiltonians with the expected splits. Also application to the backwards ray-tracing method for studying the motion of photons and shadows of black holes is possible.

Continuous gravitational wave searches with terrestrial, long-baseline interferometers are hampered by long-lived, narrowband features in the power spectral density of the detector noise, known as lines. Candidate GW signals which overlap spectrally with known lines are typically vetoed. Here we demonstrate a line subtraction method based on adaptive noise cancellation, using a recursive least squares algorithm, a common approach in electrical engineering applications such as audio and biomedical signal processing. We validate the line subtraction method by combining it with a hidden Markov model (HMM), a standard continuous wave search tool, to detect an injected continuous wave signal with an unknown and randomly wandering frequency, which overlaps with the mains power line at $60 \, {\rm Hz}$ in the Laser Interferometer Gravitational Wave Observatory (LIGO). The performance of the line subtraction method is tested on an injected continuous wave signal obscured by (a) synthetic noise data with both Gaussian and non-Gaussian components, and (b) real noise data obtained from the LIGO Livingston detector. In both cases, before applying the line subtraction method the HMM does not detect the injected continuous wave signal. After applying the line subtraction method the mains power line is suppressed by 20--40 dB, and the HMM detects the underlying signal, with a time-averaged root-mean-square error in the frequency estimate of $\sim 0.05 $ Hz. The performance of the line subtraction method with respect to the characteristics of the 60 Hz line and the control parameters of the recursive least squares algorithm is quantified in terms of receiver operating characteristic curves.

$f(Q)$ and $f(T)$ gravity are based on fundamentally different geometric frameworks, yet they exhibit many similar properties. In this article, we identify two types of background-dependent and classical correspondences between these two theories of gravity. The first correspondence is rooted in their equivalence within the background of Minkowski spacetime, while the second is based on the equivalence of their equations of motion. To establish the first correspondence, we develop the tetrad-spin formulation of $f(Q)$ gravity and we derive the corresponding expression for the spin connection. Additionally, we extract the equations of motion of $f(Q)$ gravity within this tetrad-spin framework and we elucidate the relationship through an example in spherical coordinates. For the second correspondence, we derive the general affine connection for the static and spherically symmetric spacetime in $f(Q)$ gravity, and we compare its equations of motion with the ones of $f(T)$ gravity. Amongst others, our results reveal that, within our affine connection branch, $f(T)$ solutions are not simply a subset of $f(Q)$ solutions; rather, they encompass a complex solution beyond $f(Q)$ gravity.

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability.

This study delves into the cosmological implications of the $f(Q,C)$ modified gravity framework within the context of the FLRW spacetime which offers a dynamic alternative to the standard $\Lambda$CDM cosmology. Here, we define the transit form of Hubble's parameter to explain several geometrical and physical aspects. The chosen parametric form of the Hubble parameter represents a smooth transition from the decelerating early universe to the accelerating present and late-time evolution. Employing observational datasets such as the Hubble parameter, Type Ia supernovae, Baryon Acoustic Oscillations (BAO), and Standard Candles (SC), we constrain the model parameters using the Markov Chain Monte Carlo (MCMC) method. The isotropic pressure, energy density, equation of state parameter, and energy conditions were analyzed to explore the physical viability of the $f(Q,C)$ framework. The results highlight the model's ability to replicate key cosmological behaviors, including the accelerated expansion driven by dark energy.

A small fraction of the gravitational-wave (GW) signals from binary black holes observable by ground-based detectors will be strongly lensed by intervening objects such as galaxies and clusters. Strong lensing will produce nearly identical copies of the GW signals separated in time. These lensed signals must be identified against a background of unlensed pairs GW events, some of which may appear similar by accident. This is usually done using fast, but approximate methods that, for example, check for the overlap between the posterior distributions of a subset of binary parameters, or using slow, but accurate joint Bayesian parameter estimation. In this work, we present a modified version of the posterior overlap method dubbed "PO2.0" that is mathematically equivalent to joint parameter estimation while still remaining fast. We achieve a significant gain in efficiency by incorporating informative priors about the binary and lensing populations, selection effects, and all the inferred parameters of the binary. For binary black hole signals lensed by galaxies, our improved method can detect 65% lensed events at a pair-wise false alarm probability of $\sim 2\times 10^{-6}$. Consequently, we have a 13% probability of detecting a strongly lensed event above $2.25\sigma$ significance during 18 months of observation by the LIGO-Virgo detectors at their current sensitivity. We also show how we can compute the joint posteriors of the lens and source parameters from a pair of lensed events by reweighting the posteriors of individual events in a computationally inexpensive way.

The Torsion-Bar Antenna (TOBA) is a torsion pendulum-based gravitational detector developed to observe gravitational waves in frequencies between 1 mHz and 10 Hz. The low resonant frequency of the torsion pendulum enables observation in this frequency band on the ground. The final target of TOBA is to observe gravitational waves with a 10 m detector and expand the observation band of gravitational waves. In this paper, an overview of TOBA, including the previous prototype experiments and the current ongoing development, is presented.

We present in the form of a catalogue of the cosmological perturbations within the Bahamonde- Dialektopoulos-Levi Said (BDLS) theory, which serves as the teleparallel counterpart of Horndeski gravity. To understand structure formation in cosmological models, it is essential to study both the background and perturbative aspects of their cosmology. While extensive analysis of both Horndeski gravity and its teleparallel analog exists in the literature, a quantitative understanding requires a detailed examination of their cosmological perturbations. We review here all the different gauges for the scalar, vector and tensor perturbations of a cosmological background up to second order and we hope this will help people who work with observations, to incorporate it in existing codes.

We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum gauge-fixing procedure underlying quantum-reduced loop gravity by introducing a master constraint operator on the kinematical Hilbert space of loop quantum gravity, representing a set of gauge conditions which classically constrain the densitized triad to be diagonal. The standard Hilbert space of quantum-reduced loop gravity can be recovered as a space of solutions of the master constraint operator, while on the other hand the master constraint approach provides a useful starting point for considering possible generalizations of the standard construction. We also examine the quantum dynamics of states consisting of a single six-valent node in the quantum-reduced framework. We find that the Hamiltonian which governs the dynamics of such states bears a close formal resemblance to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology.

In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of the Hamiltonian constraint on generic basis states in the Hilbert space of quantum-reduced loop gravity. Specializing to the example of the single-vertex states, we find that the Euclidean part of the Hamiltonian bears a close formal similarity to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. Extending the formal analogy to the Lorentzian part of the Hamiltonian suggests a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part, corresponding to the scalar curvature of the spatial surfaces, is not assumed to be identically vanishing, and is represented by a non-trivial operator in the quantum theory.

This research paper investigates the impact of non-metricity and matter source on the geometry of charged spheres in the presence of anisotropic matter configuration. We use a specific model of extended symmetric teleparallel theory to minimize the complexity of the field equations. Moreover, the feasible non-singular solutions are used to examine the interior composition of the charged spheres. The Darmois junction conditions are used to determine the unknown constants in the metric coefficients. We explore some significant properties in the interior of compact stars under consideration to check their viable existence in this modified framework. The equilibrium state of the charged spheres is discussed using the Tolman-Oppenheimer-Volkoff equation and stability is analyzed by sound speed and Herrera cracking approach. We find that the charged spheres in this theoretical framework are physically viable and stable.

The present work investigates the possible range of the spectral index $n_s$ and the tensor-to-scalar ratio $r$ for a sub-class of the generalized multi-scalar field inflation, which includes a linear coupling term between the multi-scalar field potential and the canonical Lagrangian. This coupling influences the slow-roll parameters and also alters our predictions for $n_{s}$ and $r$, which directly depend on those parameters. More precisely, compared to standard multi-field inflation, the values of $n_{s}$ and $r$ decrease to levels consistent with the recent Planck+BICEP/Keck constraint. Interestingly, this validates the chaotic-type potential $V=\sum_{i} \mu_{i} \phi_{i}^{p}$, which were previously ruled out in the light of the current observations.

Recently, a solution to the long-standing issue of general covariance in canonical quantum gravity has been proposed, leading to the proposal of two black hole solutions. From the above, a fundamental question arises: which solution is superior? Note that one of the solutions possesses a Cauchy horizon. Considering this quantum black hole solution with a Cauchy horizon, in the present letter, we explore whether it exhibits properties similar to those of the Reissner-Nordstr\"{o}m black hole. Given its geometric similarity, by applying the generalized Dray-'t Hooft-Redmond relation, we find evidence of mass inflation and divergence in scalar curvature, indicating that the Cauchy horizon is unstable. While this is consistent with the Strong Cosmic Censorship Conjecture, it suggests that it does not represent a regular black hole. Furthermore, we extend the metric to include a cosmological constant and study the validity of Strong Cosmic Censorship conjecture for the quantum black hole in de Sitter spacetime. The results indicate that the presence of a cosmological constant cannot prevent the violation of the conjecture when the quantum black hole approaches its extreme limit. These reasons suggest that the other black hole solution, which does not have a Cauchy horizon, is more preferable.

The ultra high frequency emission of gravitational waves by binary systems of black holes has recently been investigated in details in the framework of new experimental ideas around resonant cavities. In this article, we consider the case of elliptic trajectories. At fixed masses and frequency, we conclude that the total amount of energy radiated by the system within the bandwidth of the detector can be significantly higher than for circular orbits. However, due to subtle experimental effects, the signal-to-noise ratio is, overall, a decreasing function of the eccentricity. Limits on the maximum distance at which a merging system of black holes can be detected derived for circular orbits are therefore not improved by considering elliptic trajectories. The article is written as pedagogically as possible so as to be accessible to the non-familiar reader.

The response of a gravitational-wave (GW) interferometer is spatially modulated and is described by two antenna patterns, one for each polarization state of the waves. The antenna patterns are derived from the shape and size of the interferometer, usually under the assumption that the interferometer size is much smaller than the wavelength of the gravitational waves (long wavelength approximation, LWA). This assumption is well justified as long as the frequency of the gravitational waves is well below the free spectral range (FSR) of the Fabry-Perot cavities in the interferometer arms as it happens for current interferometers ($\mathrm{FSR}=37.5$~kHz for the LIGO interferometers and $\mathrm{FSR}=50$~kHz for Virgo and KAGRA). However, the LWA can no longer be taken for granted with third--generation instruments (Einstein Telescope, Cosmic Explorer and LISA) because of their longer arms. This has been known for some time, and previous analyses have mostly been carried out in the frequency domain. In this paper, we explore the behavior of the frequency--dependent antenna patterns in the time domain and in the time--frequency domain, with specific reference to the searches of short GW transients. We analyze the profound changes in the concept of Dominant Polarization Frame, which must be generalized in a nontrivial way, we show that the conventional likelihood-based analysis of coherence in different interferometers can no longer be applied as in current analysis pipelines, and that methods based on the null stream in triangular (60{\deg}) interferometers no longer work. Overall, this paper establishes methods and tools that can be used to overcome these difficulties in the unmodeled analysis of short GW transients.

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

Working in momentum space and at linear order in the gravitational coupling, we derive the most general class of energy-momentum tensors associated with a given multipolar structure of the spacetime in arbitrary dimensions, and built out of a mass and an angular momentum, at any order in the spin expansion. In this formalism, we are able to derive directly the full multipolar structure of any solution from the multipole expansion of the energy-momentum tensor, in complete analogy to Newtonian gravity. In particular, we identify the recurrence relations that allow obtaining the multipolar structure of the Kerr and the Myers-Perry black hole solutions, defining source multipoles in a General Relativity context for the first time. For these solutions, we are able to resum the energy-momentum tensor in momentum space at all orders in the angular momentum, and compute its real-space version. In the Kerr case we exactly obtain the matter source found by Israel, namely an equatorial, pressureless thin disk rotating at superluminal speed. For Myers-Perry in five dimensions, the matter distribution is a three-ellipsoid in four spatial dimensions with nontrivial stresses. Remarkably, for any dimensions, the matter configuration is a lower-dimensional distribution which has the same singularity structure as the fully non-linear black-hole solution. Our formalism underscores the advantage of working in momentum space to generate nontrivial matter sources for non-linear spacetimes, and could be used to construct regular non-exotic matter configurations that source spinning black hole solutions or horizonless compact objects with the same multipolar structure as black holes.

We analyse the implications of the presence of spatial curvature in modified gravity models. As it is well known, the current standard cosmological model, the $\Lambda$CDM, is assumed to be spatially flat based on the results of many experiments. However, this statement does not necessarily hold for a modified gravity (MG) model, and this leads to couplings of the spatial curvature with the parameters of the chosen cosmological model. In this paper, we illustrate the theoretical development of how spatial curvature affects the equations of motion at linear order for scalar and tensor perturbations modes using a model-independent approach based on the formalism of the Effective Field Theory (EFT) of dark energy (DE). The results show that spatial curvature gives rise to a coupling with the scalar field perturbations and the functions parameterizing the model.

In this paper, we study the motion of magnetic dipoles and electrically charged particles in the vicinity of a self-dual black hole in Loop Quantum Gravity (LQG) immersed in an external asymptotically uniform magnetic field. We explore the effects of the quantum correction parameter and electromagnetic interactions on the particle geodesics. We derive the field equations and determine the electromagnetic four-vector potential for the case of a self-dual black hole in LQG. We investigate the innermost stable circular orbits (ISCOs) for both magnetic dipoles and electrically charged particles in detail, demonstrating that the quantum correction parameter significantly influences on the ISCO radius, causing it to shrink. Additionally, we show that the ISCO radius of magnetic dipoles is greater than that of electrically charged particles due to the magnetic field interaction. We investigate the ISCO parameters (i.e., $r_{ISCO}$, $l_{ISCO}$, $\mathcal{E}_{ISCO}$, $v_{ISCO}$, and $\Omega_{ISCO}$) for magnetic dipoles and electrically charged particles, providing detailed values. Furthermore, we examine the trajectories of charged particles under various scenarios resulting from the quantum correction parameter $P$. Finally, analyzing the ISCO parameters that define the inner edge of the accretion disk, we explore the accretion disk around a self-dual black hole in LQG. We delve into the electromagnetic radiation flux, temperature, and differential luminosity as radiation properties of the accretion disk in detail. We show that the quantum correction parameter shifts the profile of the electromagnetic flux and accretion disk temperature towards the central object, leading to a slight increase in these quantities.

The integration of non-commutative geometry and Gauss-Bonnet corrections in an action and the study of their black hole responses can provide highly intriguing insights. Our primary motivation for this study is to understand the interplay of these two parameters on the geodesics of spacetime, including photon spheres and time-like orbits. In this study, we found that this integration, in its initial form, can limit the value of the Gauss-Bonnet parameter ($\alpha$), creating a critical threshold beyond which changes in the non-commutative parameter ($\Xi$) become ineffective, and the structure can only manifest as a naked singularity. Furthermore, we found that using a more complex model, which includes additional factors such as a cloud of strings and linear charge, as a sample for studying spacetime geodesics, yield different and varied results. In this scenario, negative $\alpha$ values can also play a role, notably preserving the black hole form even with a super-extremal charge ($q > m$). For $\alpha> 0.1$, the black hole mass parameter becomes significantly influential, with a critical mass below which the impact of other parameter changes is nullified. Interestingly, considering a more massive black hole, this high-mass state also maintains its black hole form within the super-extremal charge range. The existence of these two models led us to our main goal. By examining the temperature for these two cases, we find that both situations are suitable for studying the WGC. Finally, based on the behavior of these two models, we will explain how the WGC acts as a logical solution and a protector for the WCCC.

Observations of gravitational waves (GWs) from dark sirens allow us to infer their locations and distances. Galaxies, on the other hand, have precise angular positions but no direct measurement of their distances -- only redshifts. The cross-correlation of GWs, which we limit here to binary black hole mergers (BBH), in spherical shells of luminosity distance $D_L$, with galaxies in shells of redshift $z$, leads to a direct measurement of the Hubble diagram $D_L(z)$. Since this standard ruler relies only on the statistical proximity of the dark sirens and galaxies (a general property of large-scale structures), it is essentially model-independent: the correlation is maximal when both redshift and $D_L$ shells coincide. We forecast the constraining power of this technique, which we call {\it{Peak Sirens}}, for run~5~(O5) of LIGO-Virgo-KAGRA (LVK), as well as for the third-generation experiments Einstein Telescope and Cosmic Explorer. We employ thousands of full-sky light cone simulations with realistic numbers for the tracers, and include masking by the Milky Way, lensing and inhomogeneous GW sky coverage. We find that the method is not expected to suffer from some of the issues present in other dark siren methods, such as biased constraints due to incompleteness of galaxy catalogs or dependence on priors for the merger rates of BBH. We show that with Peak Sirens, given the projected O5 sensitivity, LVK can measure $H_0$ with $7\%$ precision by itself, assuming $\Lambda$CDM, and $4\%$ precision using external datasets to constrain $\Omega_m$. We also show that future third-generation GW detectors can achieve, without external data, sub-percent uncertainties in $H_0$ assuming $\Lambda$CDM, and 3\% in a more flexible $w_0w_a$CDM model. The method also shows remarkable robustness against systematic effects such as the modeling of non-linear structure formation.

We compute the linearised dispersion relations of shear waves, heat waves, and sound waves in relativistic ''matter+radiation'' fluids with grey absorption opacities. This is done by solving radiation hydrodynamics perturbatively in the ratio ''radiation stress-energy''/''matter stress-energy''. The resulting expressions $\omega \, {=} \, \omega(k)$ accurately describe the hydrodynamic evolution for any $k\, {\in}\, \mathbb{R}$. General features of the dynamics (e.g., covariant stability, propagation speeds, and damping of discontinuities) are argued directly from the analytic form of these dispersion relations.

X-ray reflection spectroscopy is a powerful tool to study the strong gravity region of black holes. The next generation of astrophysical X-ray missions promises to provide unprecedented high-quality data, which could permit us to get very precise measurements of the properties of the accretion flow and of the spacetime geometry in the strong gravity region around these objects. In this work, we test the accuracy of the relativistic calculations of the reflection model relxill and of its extension to non-Kerr spacetimes relxill_nk in view of the next generation of X-ray missions. We simulate simultaneous observations with Athena/X-IFU and LAD of bright Galactic black holes with a precise and accurate ray-tracing code and we fit the simulated data with the latest versions of relline and relline_nk. While we always recover the correct input parameters, we find residuals in the fits when the emission from the inner part of the accretion disk is higher. Such residuals disappear if we increase the number of interpolation points on the disk in the integral of the transfer function. We also simulate full reflection spectra and find that the emission angle from the accretion disk should be treated properly in this case.

We construct new infinite classes of Euclidean supersymmetric solutions of four dimensional minimal gauged supergravity comprising a $U (1) \times U (1)$-invariant, asymptotically locally hyperbolic, metric on the total space of orbifold line bundles over a spindle (bolt). The conformal boundary is generically a squashed, branched, lens space and the graviphoton gauge field can have either twist or anti-twist through the spindle bolt. Correspondingly, the boundary geometry inherits two types of rigid Killing spinors, that we refer to as twist and anti-twist for the three-dimensional Seifert orbifolds, as well as some specific flat connections for the background gauge field, determined by the data of the spindle bolt. For all our solutions we compute the holographically renormalized on-shell action and compare it to the expression obtained via equivariant localization, uncovering a markedly distinct behaviour in the cases of twist and anti-twist. Our results provide precise predictions for the large $N$ limit of the corresponding localized partition functions of three-dimensional $\mathcal{N}=2$ superconformal field theories placed on Seifert orbifolds.

Recently Hollands, Wald and Zhang proposed a new formula for the entropy of a dynamical black hole for an arbitrary theory of gravity obtained from a diffeomorphism covariant Lagrangian via the Noether charge method. We present an alternative, pedagogical derivation of the dynamical black hole entropy for $f(R)$ gravity as well as canonical scalar-tensor theory by means of conformal transformations. First, in general relativity we generalize Visser and Yan's pedagogical proof of the non-stationary physical process first law to black holes that may not be in vacuum, and give a pedagogical derivation of the second-order behavior of the dynamical black hole entropy for vacuum perturbations by considering the second-order variation of the Raychaudhuri equation. Second, we apply the derivation for general relativity to theories in the Einstein frames, and then recast the conclusions in their original frames. We show that the dynamical black hole entropy formulae of these theories satisfy both the non-stationary physical process first law and the non-stationary comparison first law via the Einstein frame. We further study the second-order behavior of the dynamical black hole entropy for vacuum perturbations, and observe that the second law is obeyed at second order in those theories. Using the Einstein frame, we also determine the relationship between the dynamical black hole entropy and the Wald entropy of the generalized apparent horizon in the original frame.

We investigate holographic complexities in the context of wedge holography, focusing specifically on black string geometry in AdS$_3$. The wedge spacetime is bounded by two end-of-the-world (EOW) branes with intrinsic Dvali-Gabadadze-Porrati (DGP) gravity. In line with this codimension-two holography, there are three equivalent perspectives: bulk perspective, brane perspective, and boundary perspective. Using both the ''Complexity=Volume'' (CV) and ''Complexity=Action'' (CA) proposals, we analyze the complexity in wedge black string geometry in the tensionless limit. By treating the branes as rigid, we find the late-time growth rates of CV and CA match exactly across bulk and brane perspectives. These results are consistent with those from JT gravity, with additional contributions from the intrinsic gravity of the branes. For fluctuating branes, we find that the late-time growth rates of CV and CA match between bulk and brane perspectives at the linear order of fluctuation. The CV results exhibit $\frac{\phi_h^2}{\phi_0}$ corrections from fluctuations, consistent with the findings in previous work. Moreover, the CA results reveal an additional constant term in the fluctuating branes case. We provide an interpretation of this in terms of gravitational edge mode effects. The distinct corrections arising from fluctuations in the CA and CV proposals suggest that the CV proposal is more sensitive to geometric details. Furthermore, we discuss these results in relation to Lloyd's bound on complexity, their general time dependence, and the effects of fluctuations.

In this paper, we delve into the thermodynamic topology of AdS Reissner-Nordstr$\ddot{o}$m (R-N) black holes by employing nonextensive entropy frameworks, specifically R$\acute{e}$nyi (with nonextensive parameter $\lambda$) and Sharma-Mittal entropy (with nonextensive parameter $\alpha, \beta$). Our investigation spans two frameworks: bulk boundary and restricted phase space (RPS) thermodynamics. In the bulk boundary framework, we face singular zero points revealing topological charges influenced by the free parameter $(\lambda)$ with a positive topological charge $(\omega = +1)$ and the total topological charge $(W = +1)$, indicating the presence of a single stable on-shell black hole. Further analysis shows that when $(\lambda)$ is set to zero, the equations align with the Bekenstein-Hawking entropy structure, demonstrating different behaviors with multiple topological charges $(\omega = +1, -1, +1)$. Notably, increasing the parameter $\alpha$ in Sharma-Mittal entropy results in multiple topological charges $(\omega = +1, -1, +1)$ with the total topological charge $(W = +1)$. Conversely, increasing $(\beta)$ reduces the number of topological charges, maintaining the total topological charge $(W = +1)$. Extending our study to the restricted phase space, we observe consistent topological charges $(\omega = +1)$ across all conditions and parameters. This consistency persists even when reducing to Bekenstein-Hawking entropy, suggesting similar behaviors in both non-extended and Hawking entropy states within RPS.

In the current era of precision cosmology, the persistence of cosmological tensions, most notably the Hubble tension and the $S_8$ tension, challenges the standard $\Lambda$CDM model. To reconcile these tensions via late-time modifications to expansion history, various features such as phantom crossing in the dark energy equation of state, a negative energy density at high redshifts, etc., are favoured. However, these scenarios cannot be realized within the framework of GR without introducing ghost or gradient instabilities. In this work, we investigate a dynamical dark energy scenario within the framework of Horndeski gravity, incorporating nonminimal coupling to gravity and self-interactions. We highlight that the model can exhibit novel features like phantom crossing and negative dark energy densities at high redshifts without introducing any instabilities. For this specific Horndeski model, we perform a comprehensive analysis of the background evolution along with the effects on perturbations, examining observables like growth rate, matter and CMB power spectrum. To check the consistency of the model with the observational data, we employ MCMC analysis using BAO/$f\sigma_8$, Supernovae, and CMB data. While the model does not outperform the standard $\Lambda$CDM framework in a combined likelihood analysis, there remains a preference for non-zero values of the model parameters within the data. This suggests that dynamical dark energy scenarios, particularly those with non-minimal couplings, merit further exploration as promising alternatives to GR, offering rich phenomenology that can be tested against a broader range of current and upcoming observational datasets.

We analyze solutions of Chamseddine's topological gravity in four space-time dimensions and discover various black hole solutions with(out) torsion as well as those that describe naked singularities. Because all of the solutions belong to the sector with vanishing scalar fields, they share peculiar trait that all conserved charges are vanishing.

We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions are in fact linked in multiple ways, and can be seen as different aspects of the same research programme. This research programme has two main physical goals and one general conceptual aim. The physical goals are to move beyond the two idealizations/approximations of asymptotic or closed boundary conditions in gravitational physics and of ideal reference frames (coded in coordinate frames or gauge fixings), thus achieving a more realistic modeling of (quantum) gravitational physical phenomena. The conceptual aim is to gain a better understanding of the influence of observers in physics and the ensuing limits of objectivity.

We introduce a new method designed for Bayesian inference of the angular power spectrum of the Gravitational Wave Background (GWB) anisotropy. This scheme works with time-series data and can optionally incorporate the cross-correlations between the GWB anisotropy and other cosmological tracers, enhancing the significance of Bayesian inference. We employ the realistic LISA response and noise model to demonstrate the validity of this approach. The findings indicate that, without considering any cross-correlations, the 4-year LISA data is insufficient to achieve a significant detection of multipoles. However, if the anisotropies in the GWB are strongly correlated with the Cosmic Microwave Background (CMB), the 4-year data can provide unbiased estimates of the quadrupole moment ($\ell = 2$). This reconstruction process is generic and not restricted to any specific detector, offering a new framework for extracting anisotropies in the GWB data from various current and future gravitational wave observatories.

The Abelian gauge symmetry proposed by Hermann Weyl is generalized to its non-Abelian extension. Afterwards the standard model is generalized to incorporate the Abelian and non-Abelian Weyl symmetry. This symmetry extension brings new gauge particles that can be potential candidates for the dark matter. It also naturally introduces a second scalar field into the theory. The breaking of the Weyl symmetry turns this scalar field into a dimensional constant, making the Higgs as the only scalar component in the standard model. In addition to the expected benefits, there are three unexpected bonuses: (1) it brings some new understanding of the parity violation; (2) it provides an answer to the sign problem in the Higgs mechanism; (3) it gives some new perspectives on the nature of the neutrino: non-Abelian Weyl symmetry demands that there \textit{must be} right-handed netrino; furthermore, the smallness of the neutrino mass is protected by the non-Abelian Weyl symmetry.

We provide a reply to the Argument from Intimacy on behalf of defenders of emergent spacetime in theories of quantum gravity. We argue that if one accepts that spacetime regions are nowhere in the sense that they are locations but do not have locations, then the Argument from Intimacy can be resolved. We go on to consider a problem with this response, namely that it is unavailable to super-substantivalists. We argue that this is right for identity but not priority super-substantivalists. We then suggest that there is no cost for our solution here, since identity versions of super-substantivalism face severe challenges in the context of spacetime emergence and so should be rejected anyway.

Ultralight bosonic wave dark matter (DM) is preponderantly contesting the conventional cold DM paradigm in predicting diverse and rich phenomena on small scales. For a DM halo made of ultralight bosons, the wave interference naturally induces slow de Broglie time-scale fluctuations of the gravitational potential. In this paper, we first derive an estimation for the effect of a time-varying gravitational potential on photon propagation. Our numerical simulations suggest that the time-varying potential of a $10^{11}M_{\odot}$ halo composed of $10^{-22}\,\mathrm{eV}$ bosons would stretch or compress a time series signal by a factor of $10^{-10}$. Here, we propose that, due to the precise measurements of their arrival times, lensed repeating fast radio bursts (FRBs) have the potential to effectively validate temporal variations in gravitational potential by monitoring their images over a period of approximately $\mathcal{O}(1)$ years. With rapidly growing FRB observations, this method would serve as a promising method to directly probe the wave nature of galactic DM halos.

The confinement of quarks is analyzed by establishing a correspondence between the effective actions inside a black hole and the QCD action, formulated as a scalar field theory in the Carrollian regime. We first demonstrate that both QCD (in the instanton-dominance limit) and the interior of a black hole can be described at one-loop as the effective action of a soliton in the Carrollian limit. At one-loop, QCD confinement is shown to be entirely analogous to confinement within a black hole, with the event horizon acting as the hadron radius. Higher-order corrections to the effective action do not destabilize the solitons but may produce subtle observable effects, such as deconfinement or a partial resolution to the information loss problem.

We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov-Poisson system and to the Einstein-Vlasov system. There are several reasons why a mathematical analysis of this numerical scheme is important. A generalization of the present result to the case of flat axially symmetric solutions would prove that the steady states obtained numerically in \cite{AR3} do exist. Moreover, in the relativistic case the question whether a steady state can be obtained by this scheme seems to be related to its dynamical stability. This motivates the desire for a deeper understanding of this strategy.

From a study of the subleading structure of the asymptotic equations of motion in Einstein-Yang-Mills theory, we construct charges that are conserved up to quadratic order in non-radiative vacuum. We then show that these higher spin charges obey the celestial $sw_{1+\infty}$ symmetry algebra found earlier from the OPE of positive-helicity conformally soft gluons and gravitons.

We apply an Internal Robustness (iR) analysis to the recently released Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillations dataset. This approach examines combinations of data subsets through a fully Bayesian model comparison, aiming to identify potential outliers, subsets possibly influenced by systematic errors, or hints of new physics. Using this approach, we identify three data points at $z= 0.295,\,0.51,\,0.71$ as potential outliers. Excluding these points improves the internal robustness of the dataset by minimizing statistical anomalies and enables the recovery of $\Lambda$CDM predictions with a best-fit value of $w_0 = -1.050 \pm 0.128$ and $w_a = 0.208 \pm 0.546$. These results raise the intriguing question of whether the identified outliers signal the presence of systematics or point towards new physics.