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The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations and of low values of the black hole spin parameter and deformation parameters. We find that the deformation parameter $\alpha_{13}$ has a stronger impact on the quasi-normal modes than the other leading order deformation parameters ($\alpha_{22}$, $\alpha_{52}$, and $\epsilon_{3}$). We derive a fitting formula for the fundamental modes with $l=2$ and $l=3$ for the deformation parameter $\alpha_{13}$ valid in the slow rotation approximation ($a_* < 0.4$). Finally, we constrain $\alpha_{13}$ from the event GW170104; within our analysis, we find that the data of GW170104 are consistent with the predictions of GR., Comment: 16 pages, 7 figures

According to the celebrated singularity theorems, space-time singularities in general relativity are inevitable. However, it is generally believed that singularities do not exist in nature, and their existence suggests the necessity of a new theory of gravity. In this paper, we investigated a regular astrophysically viable space-time (regular in the sense that it is singularity-free) from the observational point of view using observations from the LIGO, Virgo, and KAGRA (LVK), and the event horizon telescope (EHT) collaborations. This black hole solution depends on a free parameter $\ell$ in addition to the mass, $M$, and the spin, $a$, violating, in this way, the non-hair theorem/conjecture. In the case of gravitational wave observations, we use the catalogs GWTC-1, 2, and 3 to constrain the free parameter. In the case of the EHT, we use the values of the angular diameter reported for SgrA* and M87*. We also investigated the photon ring structure by considering scenarios such as static spherical accretion, infalling spherical accretion, and thin accretion disk. Our results show that the EHT observations constrain the free parameter $\ell$ to the intervals $0\leq \ell \leq 0.148$ and $0\leq \ell \leq 0.212$ obtained for SgrA* and M87*, respectively. On the other hand, GW observations constrain the free parameter with values that satisfy the theoretical limit, particularly those events for which $\ell<<1$. Our results show that the most stringent constraints on $\ell$ correspond to the events GW191204-171526 ($\ell=0.041^{+0.106}_{-0.041}$) and GW190924-021846 ($\ell=0.050^{+0.165}_{-0.050}$) for the SEOB model., Comment: 25 pages, 15 figures

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

We present a relativistic disk reflection model based on the geometry calculated using analytical formulae for super-Eddington accretion flows. This model features a slim disk geometry where the inner disk thickness is proportional to radius, becoming thicker as the mass accretion rate increases. The slim disk profile reduces the brightness of the blue horn in the Fe K emission line for a fixed emissivity and significantly changes the intensity profile for a lamppost geometry. The model is constructed assuming a spherically symmetric spacetime. It can be used for any kind of sources showing fluorescent reflection features and predicted to have slim accretion disks, like slow rotating black holes in X-ray binaries, active galactic nuclei, tidal disruption events, and neutron star X-ray binaries. To show the capability of the model, we use the 2017 \textit{NICER} and \textit{NuSTAR} data of the ultraluminous X-ray transient Swift~J0243.6+6124., Comment: 9 pages, 4 figures

The theory of general relativity (GR) is the standard framework for the description of gravitation and the geometric structure of spacetime. With the recent advancement of observational instruments, it has become possible to probe the strong field regime to test GR. We present the constraints obtained from the binary black hole inspiral data of the LIGO-Virgo-Kagra (LVK) gravitational wave (GW) observations on the deformations of some popular parametrized non-Kerr metrics., Comment: 7 pages, 1 figure. Prepared for the proceeding of the seventh international workshop on the TianQin science mission

The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW) follow the Kerr spacetime as the theoretical foundation. Hence, any possible deviations from the Kerr spacetime around BHs serve as a test of the nature of gravity in the strong-field regime and of the predictions of General Relativity. In our study, we perform a theory-agnostic test of the Kerr hypothesis using BBH inspirals from the third Gravitational-wave Transient Catalog (GWTC-3). Considering the Johannsen metric, we compute the leading-order deviation to the emitted GW in the frequency domain. Our results provide constraints on two deformation parameters ($\alpha_{13}$ and $\epsilon_3$) and demonstrate the degeneracy between these two non-Kerr parameters., Comment: 10 pages, 6 figures. Supplemental material (16 pages, 16 figures) available from the authors upon reasonable request

In the disk-corona model, the X-ray spectrum of a stellar-mass black hole in an X-ray binary is characterized by three components: a thermal component from a thin and cold accretion disk, a Comptonized component from a hot corona, and a reflection component produced by illumination of the cold disk by the hot corona. In this paper, we assume a lamppost corona and we improve previous calculations of the X-ray spectrum of black hole X-ray binaries. The reflection spectrum is produced by the direct radiation from the corona as well as by the returning radiation of the thermal and reflection components and is calculated considering the actual spectrum illuminating the disk. If we turn the corona off, the reflection spectrum is completely generated by the returning radiation of the thermal component, as it may happen for some sources in soft spectral states. After choosing the radial density profile of the accretion disk, the ionization parameter is calculated self-consistently at any radial coordinate of the disk from the illuminating X-ray flux and the local electron density. We show the predictions of our model in different regimes and we discuss its current limitations as well as the next steps to improve it., Comment: 10 pages, 6 figures. v2: refereed version

We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of RELXILL (modified to read the table of REFLIONX, which is the non-relativistic reflection model used in our calculations). We find that RELXILL with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk's ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases., Comment: 19 pages, 14 figures. v2: refereed version

Physically relevant solutions in general relativity often contain spacetime singularities, which are typically interpreted as a sign of breakdown of the theory at high densities/curvatures. Hence, there has been a growing interest in exploring phenomenological scenarios that describe singularity-free black holes, gravitational collapses, and cosmological models. We examine the metric put forth by Mazza, Franzin \& Liberati for a rotating regular black hole and estimate the regularization parameter $l$ based on existing X-ray and gravitational wave data for black holes. When $l=0$, the solution corresponds to the singular Kerr solution of general relativity, while a non-zero value of $l$ yields a regular black hole or a regular wormhole. The analysis reveals that the available data support a value of $l$ that is close to zero., Comment: 2 pages, contribution to the 2023 Gravitation session of the 57th Rencontres de Moriond

The past 10 years have seen tremendous progress in our capability of testing General Relativity in the strong field regime with black hole observations. 10 years ago, the theory of General Relativity was almost completely unexplored in the strong field regime. Today, we have gravitational wave data of the coalescence of stellar-mass black holes, radio images of the supermassive black holes SgrA$^*$ and M87$^*$, and high-quality X-ray data of stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. In this manuscript, we will review current efforts to test General Relativity with black hole X-ray data and we will provide a detailed description of the public codes available on ABHModels., Comment: 31 pages, 5 figures. Talk given at the Frascati Workshop 2023 "Multifrequency Behaviour of High Energy Cosmic Sources - XIV" (Palermo, Italy, 12-17 June 2023). v2: refereed version

X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we use a general relativistic magnetohydrodynamic (GRMHD) code to generate a thin accretion disk in Kerr spacetime and ray-tracing techniques to calculate its relativistically broadened reflection spectrum. We simulate NuSTAR observations and we test the capability of current reflection models based on Novikov-Thorne disks to recover the correct input parameters. Our study shows that we can measure the correct input parameters in the case of high inclination angle sources, while we find some minor discrepancy when the inclination angle of the disk is low., Comment: 10 pages, 10 figures. v2: refereed version

The presence of spacetime singularities in physically relevant solutions of the Einstein Equations is normally interpreted as a symptom of the breakdown of classical general relativity at very high densities/curvatures. However, despite significant efforts in the past decades, we do not have yet any robust theoretical framework to solve the problem of spacetime singularities. In this context, the past few years have seen an increasing interest in the study of phenomenological scenarios to describe singularity-free black holes, gravitational collapses, and cosmological models. In the present work, we consider the recent proposal by Mazza, Franzin & Liberati for a rotating regular black hole and we measure their regularization parameter $l$ from the available X-ray and gravitational wave black hole data. For $l = 0$, we recover the singular Kerr solution of general relativity, while for $l \neq 0$ we can have a regular black hole or a regular wormhole. Our analysis shows that the available data are consistent with a vanishing regularization parameter $l$ and we can constrain its value. From a NuSTAR spectrum of the Galactic black hole in EXO 1846-031, we find $l/M < 0.49$ (90% CL). From the gravitational wave event GW190707A, we find $l/M < 0.72$ (90% CL)., Comment: 31 pages, 10 figures. v3: refereed version. v4: clarified a couple of passages

Gravitational-wave observations of binary black holes provide a suitable arena to test the fundamental nature of gravity in the strong-field regime. Using the data of the inspiral of 29 events detected by the LIGO-Virgo observatories, we perform a theory-agnostic test of the Kerr hypothesis. We compute the leading-order deviation to the gravitational waves emitted in the frequency domain and provide constraints on two deformation parameters ($\delta_1$ and $\delta_2$) belonging to a general class of axisymmetric non-Kerr black hole spacetimes proposed by Konoplya, Rezzolla & Zhidenko. Our study shows that all the analyzed events are consistent with the Kerr hypothesis. The LIGO-Virgo data provide stronger constraints on $\delta_1$ and $\delta_2$ than those obtained in our previous studies with X-ray data (Papers I and II), while, on the other hand, they cannot constrain the other deformation parameters of the Konoplya-Rezzolla-Zhidenko metric ($\delta_3$, $\delta_4$, $\delta_5$, and $\delta_6$)., Comment: 11 pages, 2 figures. v2: refereed version

In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars. Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental ($f$)-mode frequency for realistic equations of state (EoS). We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of $1.2 - 2.0$ $M_{\odot}$) for each of these EoS. Using the gravitational waveform obtained from the simulations we extract the $f$-modes of the stars. The obtained results are tested against the pre-existing perturbation methods and find good agreement. Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches. We also show that even using perturbed single star simulations can provide good agreement with $f$-modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive., Comment: 24 pages, 9 figures. refereed version