With the help of Newman-Janis method new spinning black hole (BH) solution for a non-local gravity model was obtained. We show how to account the quantum gravitational correction part in BH shadows modelling using spinning BH metrics with a model independent approach. It is confirmed that in the future to follow the increasing of the experimental accuracy and therefore to reproduce new results theoretically one could take into account different field correction terms instead of introducing of new fields and/or curvature expansions.

This study looks into regular solutions in a theory of gravity called $f(R)$ gravity, which also involves a scalar field. The $f(R)$ theory changes Einstein's ideas by adding a new function related to something called the Ricci scalar. This lets us tweak the equations that describe how gravity works. Adding a scalar field makes the theory more interesting, giving us more ways to investigate and understand it. { The main goal of this research is to create regular black holes using a combination of $f(R)$ gravitational theory and a scalar field.} Regular solutions don't have any singularities, which are points where certain physical quantities, like invariants, become really big or undefined. { In this context, we find two regular black hole solutions by using a spherical space with either an equal or unequal approach.} For the solutions where we use the equal approach, we figure out the shape of $f(R)$ and how it changes, along with its first and second derivatives. We demonstrate that Hayward's solution in this theory stays steady because all the shapes of $f(R)$ and their first and second derivatives are positive. Next, we focus on the case where the metric isn't equal and figure out the black hole solution. We also find out what $f(R)$ and the scalar field look like in this situation. We demonstrate that the solution in this case is a broader version of the Hayward solution. When certain conditions are met, we end up back at the scenario where the metrics are equal. We also prove that this model is stable because $f(R)$, along with its first and second derivatives, are all positive. { We analyze the trajectories of these black hole solutions and determine the forms of their conserved quantities that remain same along those trajectories.

All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr solution comes with several difficulties such as the existence of Cauchy horizons, curvature singularities, and causality-violating regions. Attempts to resolve some of these issues include phenomenological BH models, which typically contain nontrivial matter content. We introduce a simple framework here to examine the properties of matter in such phenomenological models for a broad class of stationary and axisymmetric spinning BH spacetimes, generated from nonspinning seed solutions via a metric ansatz. We apply this framework to a representative set of spinning BH spacetimes and the non-spinning seeds from which they are derived. The models span different types of matter - fluids, scalar fields, electromagnetic fields. For each model, we calculate the timelike four-velocity of the matter and thereby identify the rest frame of the matter, both outside and inside the horizon. We then examine the spatial distribution of the matter rest-frame energy density $\epsilon$ and the principal pressures. This provides a complete picture of how the matter moves, what its material properties are, and whether it obeys the classical energy conditions. Notably, at a horizon, the normal component of the pressure always satisfies $p_n = -\epsilon$. We also investigate the expansions of the principal null congruences and explore the Hawking mass profiles of these spacetimes. These provide glimpses into the geometry of the stationary BH exterior as well as the nonstationary interior cosmology. The axisymmetric metric ansatz we work with can be used to generate new spinning solutions from a variety of nonspinning seeds. The matter in these models often satisfies the weak energy condition, at least in the BH exterior, and some models exhibit non-rigid, differential rotation.

Next-generation gravitational-wave detectors, such as the Einstein Telescope (ET), are expected to observe a few 100,000 signals each year. This will require efficient analysis tools and computational resources well beyond the needs of current detectors. Such resources are not presently available to the science community. Therefore, to investigate ET observational capabilities and science cases, Fisher-matrix methods are used to predict how precisely parameters like mass, spin, source distance or sky location can be estimated from ET data. The approach is based on a Gaussian approximation of the likelihood function. However, the reliability of error estimates obtained from Fisher-matrix methods remains an open question. In this article, we present a Fisher-matrix analysis of signals of the Gravitational Wave Transient Catalog (GWTC). We compare parameter-estimation errors obtained using the Fisher matrix code GWFish with the errors from the marginal distributions of the Virgo/LIGO posterior analysis. In order to understand the impact of prior distributions on the results, we implemented a Gaussian likelihood sampling algorithm with priors in GWFish. To ensure a fair comparison of the methods, the GWFish analyses presented in this article use the same priors and the same instrument-noise spectra as the Virgo/LIGO posterior analyses. Our findings imply that Fisher-matrix methods, especially if augmented with the use of priors, are a valid tool for ET science-case studies.

In this article, we investigate the impact of cosmological parameters on black holes using an exact solution to Einstein's equations that satisfies the Whittaker equation of state. We examine a spherically symmetric black hole in the background of a static Einstein Universe with a perfect fluid source with the cosmological constant. This solution is characterized by two independent parameters, namely the size of the universe~($R$) and the cosmological constant~(Lambda), representing the cosmological influences. We explore phenomena such as periastron precession and the scattering of massless scalar fields to determine how these cosmological parameters affect the physics around black holes.

In the framework of black hole perturbation theory, this work investigates the standing wave solutions in Reissner-Nordtsr\"om (RN) anti-de Sitter (AdS) spacetimes with a naked singularity. These solutions can be viewed as a specific class of quasinormal modes exhibiting distinct characteristics. The imaginary parts of their frequencies are numerically vanishing, allowing them to persist over an extended period. Besides, these modes are predominantly stationary in terms of the evolution of spacetime waveforms. The numerical calculations are carried out employing the finite difference method, and the quasinormal frequencies extracted by the Prony method are shown to be consistent with those obtained using the matrix method. The obtained waveforms and quasinormal frequencies are shown to be drastically different from those of an extreme RN-AdS black hole. As the quasinormal modes are primarily dissipative, the non-dissipative standing waves are attributed to the nature that the singularity can neither be a sink nor a source of the gravitational system.

Gravitational waves from condensates of ultra-light particles, such as axion, around rotating black holes are a promising probe to search for unknown physics. For this purpose, we need to characterize the signal to detect the gravitational waves, which requires tracking the evolution of the condensates, including various effects. The axion self-interaction causes the non-linear coupling between the superradiant modes, resulting in complicated branching of evolution. Most studies so far have considered evolution under the non-relativistic approximation or the two-mode approximation. In this paper, we numerically investigate the evolution of the axion condensate without these approximations, taking higher multipole modes into account. We also investigate the possible signature in gravitational waves from the condensate. We show that the higher multipole modes are excited, leading to the gravitational wave signal by the transition of the axion between different levels. The most prominent signal of gravitational waves arises from the transition between modes with their angular quantum numbers different by two. The gravitational wave signal is emitted in the deci-Hz band for stellar mass black holes, which might be observable with the future gravitational wave detectors.

Symmetric teleparallel gravity (STG) is a gravity theory which takes non-metricity tensor to describe gravity effects. In the STG framework, we study the conformal equivalent scalar-tensor theory of f(Q) model and calculate the cosmological linear perturbations of the conformal transformed action. We confirm the result already present in references that f(Q) gravity shows different degrees of freedom on different backgrounds at linear perturbation level. We also explain that this situation often means the linear perturbation theory breaks down and the model may suffer from strong coupling problem.

We study the axial gravitational perturbations of slowly-rotating compact objects which are assumed to be supported by anisotropic fluids. We find that the gravitational perturbations decouple from the matter perturbations for axial sectors. We obtain a master wave equation whose potential is fully determined by the metric functions. This equation makes the calculations of gravitational QNMs for rotating compact objects extremely easy in specific background configurations.

Apparent horizon plays an important role in numerical relativity as it provides a tool to characterize the existence and properties of black holes on three-dimensional spatial slices in 3+1 numerical spacetimes. Apparent horizon finders based on different techniques have been developed. In this paper, we revisit the apparent horizon finding problem in numerical relativity using multigrid-based algorithms. We formulate the nonlinear elliptic apparent horizon equation as a linear Poisson-type equation with a nonlinear source, and solve it using a multigrid algorithm with Gauss-Seidel line relaxation. A fourth order compact finite difference scheme in spherical coordinates is derived and employed to reduce the complexity of the line relaxation operator to a tri-diagonal matrix inversion. The multigrid-based apparent horizon finder developed in this work is capable of locating apparent horizons in generic spatial hypersurfaces without any symmetries. The finder is tested with both analytic data, such as Brill-Lindquist multiple black hole data, and numerical data, including off-centered Kerr-Schild data and dynamical inspiraling binary black hole data. The obtained results are compared with those generated by the current fastest finder AHFinderDirect (Thornburg, Class. Quantum Grav. 21, 743, 2003), which is the default finder in the open source code Einstein Toolkit. Our finder performs comparatively in terms of accuracy, and starts to outperform AHFinderDirect at high angular resolutions (\sim 1^\circ) in terms of speed. Our finder is also more flexible to initial guess, as opposed to the Newton's method used in AHFinderDirect. This suggests that the multigrid algorithm provides an alternative option for studying apparent horizons, especially when high resolutions are needed.

Accurate information from gravitational wave signals from coalescing binary neutron stars provides essential input to downstream interpretations, including inference of the neutron star population and equation of state. However, even adopting the currently most accurate and physically motivated models available for parameter estimation (PE) of BNSs, these models remain subject to waveform modeling uncertainty: differences between these models may introduce biases in recovered source properties. In this work, we describe injection studies investigating these systematic differences between the two best waveform models available for BNS currently, NRHybSur3dq8Tidal and TEOBResumS. We demonstrate that for BNS sources observable by current second-generation detectors, differences for low-amplitude signals are significant for certain sources.

In this paper, we introduce a metric ansatz for describing spherically symmetric quantum corrected black hole (BH) space-time within an AdS background, incorporating both ordinary and phantom global monopoles. Afterwards, we focus into the thermodynamic properties of this BH, calculating essential parameters such as the Hawking temperature and the specific heat capacity. Moving forward, we analyze the effective potential of the system for both null and time-like geodesics, as well as the shadow radius of the BH. Additionally, we compute the emission rate of particles from this BH. Finally, we explore the geodesic equations of motion and visualize the trajectories of massive particles within the BH. Throughout our investigation, we examine how the presence of ordinary and phantom global monopoles, alongside the quantum corrected parameter, influences various thermal properties, the effective potential of the system, the BH shadow radius, energy emission rate, and the trajectories of massive particles. Importantly, through the generation of figures depicting these phenomena, we highlight the distinctions between results obtained with ordinary global monopoles and phantom ones, across a range of quantum corrected parameter values considering small values of the energy scale parameter.

With the strong evidence for a gravitational wave (GW) background in the nanohertz frequency band from pulsar timing arrays, the detection of continuous GWs from individual supermassive black hole binaries is already at the dawn. Utilizing continuous GWs to test theories of gravity, especially to test the polarizations of GWs is becoming more and more realistic. In this theoretical study, assuming a detection of signals from individual supermassive binary black holes, we use the null stream to estimate the capability of identifying the nontensorial polarizations of GWs. We consider cases for the nontensorial polarizations where the dipole radiation and quadrupole radiation dominate separately. With a frequentist method, we estimate the threshold of the nontensor-to-tensor relative amplitude above which extra polarizations can be detected. We also conduct Bayesian analysis to do parameter estimation with the null stream data. Our treatment provides a data-analysis methodology using the null stream to probe the nontensorial GW polarizations with pulsar timing arrays.

Recent surveys have been reporting bulk peculiar flows considerably faster than expected. Bulk flows are moving matter and matter in motion implies nonzero energy flux. In relativity, as opposed to Newtonian physics, matter fluxes gravitate as well, since they also contribute to the energy-momentum tensor. The gravitational input of the "peculiar" flux survives at the linear level and it can drastically change our understanding of the way bulk flows have evolved in time. By default, the Newtonian analysis of peculiar motions bypasses the relativistic flux-contribution to the gravitational field. The problem is that there are also studies, with an otherwise relativistic profile, which inadvertently do the same. As result, these treatments reduce to Newtonian and they misleadingly reproduce the slow Newtonian growth-rate of linear peculiar velocities. In contrast, by accounting for the flux effects, the proper relativistic analysis arrives at a considerably stronger growth. We show that it is the flux input of the moving matter to gravity that separates the relativistic studies of peculiar motions from the rest and, in so doing, it could provide an answer to the bulk-flow question.

We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a system of partial differential equations of any order, and show that the Einstein equations in Bondi-like coordinates in their second-order form used in numerical relativity do not meet it, in agreement with results of Giannakopoulos et al for specific first-order reductions. In the principal part, frozen coefficient approximation that one uses to examine hyperbolicity, we explicitly construct the general solution to identify the solutions that obstruct strong hyperbolicity. Independently, we present a first-order symmetric hyperbolic formulation of the Einstein equations in Bondi gauge, linearised about Schwarzschild, thus completing work by Frittelli. This establishes an energy norm ($L^2$ in the metric perturbations and selected first and second derivatives), in which the initial-boundary value problem, with initial data on an outgoing null cone and boundary data on a timelike cylinder or an ingoing null cone, is well-posed, thus verifying a conjecture by Giannakopoulos et al. Unfortunately, our method does not extend to the pure initial-value problem on a null cone with regular vertex.

We investigate the measurement correlation between the effective spin and the effective tidal deformability in gravitational wave signals from binary neutron star mergers. We exploit the fact that the tidal effects in a binary system are prominent when the components are closer during the late-inspiral. Thus, we indicate to a computationally efficient strategy of extracting the tidal information compressed within seconds before the merger. We report our observations for \texttt{GW170817} and explore the suitability of our approach for the upcoming observation scenarios. Fast and accurate measurements of the tidal deformability parameters can be used to inform astronomers in prioritizing the electromagnetic follow-up efforts for such sources.

It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this paper begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wavefunctions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The paper closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but "one-shot" entropy differences do.

Through use of the Pauli-Villars regulator procedure we construct a second- plus fourth-order-derivative theory of gravity that serves as an ultraviolet completion of standard second-order-derivative quantum Einstein gravity that is ghost-free, unitary and power counting renormalizable.

A binary stellar system that ventures too close to a supermassive black hole can become tidally separated. In this article, we investigate the role of relativistic effects in these encounters through 3-body simulations. We use the Hybrid Relativistic-Newtonian Approximation (HRNA), which combines the exact relativistic acceleration from a Schwarzschild black hole with a Newtonian description of the binary's self-gravity. This method is compared against Newtonian and Post-Newtonian (1PN) simulations. Our findings show good agreement between HRNA and 1PN results, both of which exhibit substantial differences from Newtonian simulations. This discrepancy is particularly pronounced in retrograde encounters, where relativistic simulations predict up to $30\%$ more separation events and an earlier onset of binary separation ($\beta=2$ compared to $2.5$ in Newtonian simulations, with $\beta$ the impact parameter). Additionally, the HRNA model predicts about 15$\%$ more potential extreme mass ratio inspirals and generate a higher number of hypervelocity star candidates, with velocities up to 2,000 km/s faster than those predicted from Newtonian simulations. Furthermore, compared to Newtonian cases, relativistic encounters are more likely to result in direct stellar collisions and binary mergers.

We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds into isometric submanifolds. We then suggest a definition of spectral subtriple based on the notion of submanifold algebra and the already existing notions of Riemannian, isometric, and totally geodesic morphisms. We have shown that our definitions work at least in some relevant almost commutative examples.

Nested sampling parameter estimation differs from evidence estimation, in that it incurs an additional source of error. This error affects estimates of parameter means and credible intervals in gravitational wave analyses and beyond, and yet, it is typically not accounted for in standard error estimation methods. In this paper, we present two novel methods to quantify this error more accurately for any chain based nested sampler, using the additional likelihood calls made at runtime in producing independent samples. Using injected signals of black hole binary coalescences as an example, we first show concretely that the usual error estimation method is insufficient to capture the true error bar on parameter estimates. We then demonstrate how the extra points in the chains of chain based samplers may be carefully utilised to estimate this error correctly, and provide a way to check the accuracy of the resulting error bars. Finally, we discuss how this error affects $p$-$p$ plots and coverage assessments.

The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technical problems in numerical simulations. We solve this hierarchical growth problem by preconditioning the flow so that the growth rate becomes identical for every eigenmode. As an example, we show that the preconditioned flow enables us to investigate the real-time quantum evolution of an anharmonic oscillator with the system size that can hardly be achieved by using the original flow.

The Event Horizon Telescope (EHT) has revolutionized our ability to study black holes by providing unprecedented spatial resolution and unveiling horizon-scale details. With advancements leading to the next-generation EHT, there is potential to probe even deeper into the black hole's dark region, especially the inner shadow characterized by low-intensity foreground emissions from the jet, thanks to a significant enhancement in dynamic range by two orders of magnitude. We demonstrate how such enhanced observations could transform supermassive black holes into powerful probes for detecting annihilating dark matter, which can form a dense profile in the vicinity of supermassive black holes, by examining the morphology of the black hole image.