2023-1106

• [2311.01911] Astrophysical black holes: theory and observations
Abstract: These notes cover part of the lectures presented by Andrea Maselli for the 59th Winter School of Theoretical Physics and third COST Action CA18108 Training School 'Gravity -- Classical, Quantum and Phenomenology'. The school took place at Palac Wojanów, Poland, from February 12th to 21st, 2023. The lectures focused on some key aspects of black hole physics, and in particular on the dynamics of particles and on the scattering of waves in the Schwarzschild spacetime. The goal of the course was to introduce the students to the concept of black hole quasi normal modes, to discuss their properties, their connection with the geodesic motion of massless particles, and to provide numerical approaches to compute their actual values.

Keywords: review; black hole; QNM

2023-1107

• [2311.02138] A regular metric does not ensure the regularity of spacetime
Abstract: In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There is work in the literature that assumes that the regularity of the metric is a sufficient condition to guarantee it. We study three regular metrics and show that they have singular spacetime. We also show that these metrics can be interpreted as solutions for black holes whose matter source is described by nonlinear electrodynamics. We analyze the geodesic equations and the Kretschmann scalar to verify the existence of the curvature singularity. Moreover, we use a change of the line element , which is a process of regularization of spacetime already known in the literature. We then recompute the geodesic equations and the Kretschmann scalar and show that all metrics now have regular spacetime. This process transforms them into black-bounce solutions, two of which are new. We have discussed the properties of the event horizon and the energy conditions for all models.

Keywords: regular black hole

2023-1108

• [2311.03474] Observing gravitational waves with solar system astrometry
Abstract: The subtle influence of gravitational waves on the apparent positioning of celestial bodies offers novel observational windows. We calculate the expected astrometric signal induced by an isotropic Stochastic Gravitational Wave Background (SGWB) in the short distance limit. Our focus is on the resultant proper motion of Solar System objects, a signal on the same time scales addressed by Pulsar Timing Arrays (PTA). We derive the corresponding astrometric deflection patterns, finding that they manifest as distinctive dipole and quadrupole correlations, or in some cases, may not be present. Our analysis encompasses both Einsteinian and non-Einsteinian polarisations. We estimate the upper limits for the amplitude of a scale-invariant SGWB that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. With the Gaia satellite and the Vera C. Rubin Observatory poised to track an extensive sample of asteroids-ranging from  to , we highlight the significant future potential for similar surveys to contribute to our understanding of the SGWB.

Keywords: solar system; GW

• [2311.04050] Topological Interpretation Black Hole Phase Transition in Gauss-Bonnet Gravity
Abstract: Black holes are treated as topological defects in the thermodynamic parameter space of Einstein-Gauss-Bonnet gravity theory. The kinetics of thermodynamic defects are studied using Duan's bifurcation theory. In this picture, a first-order phase transition between small/large black hole phases is interpreted as the interchange of winding numbers between the defects as a result of some action at a distance. We observe a first-order phase transition between small/large black holes for D=5 Gauss-Bonnet theory similar to Reissner-Nordström black holes in AdS space. This implies that these black hole solutions share the same topology and phase structure. We have also studied the phase transition of neutral black holes in D≥6 and found a transition between unstable small and large stable black hole phases similar to the case of neutral black holes in AdS space. It has been conjectured that black holes with similar topological nature exhibit the same thermodynamic properties. Our results strengthen the conjecture by connecting topology to phase transitions.

Keywords: small/large black hole; phase transition

2023-1113

• [2311.05983] Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
Abstract: Direct detection of gravitational waves and binary black hole mergers have proven to be remarkable investigations of general relativity. In order to have a definitive answer as to whether the black hole spacetime under test is the Kerr or non-Kerr, one requires accurate mapping of the metric. Since EMRIs are perfect candidates for space-based detectors, Laser Interferometer Space Antenna (LISA) observations will serve a crucial purpose in mapping the spacetime metric. In this article, we consider such a study with the Johannsen spacetime that captures the deviations from the Kerr black hole and further discuss their detection prospects. We analytically derive the leading order post-Newtonian corrections in the average loss of energy and angular momentum fluxes generated by a stellar-mass object exhibiting eccentric equatorial motion in the Johannsen background. We further obtain the orbital evolution of the inspiralling object within the adiabatic approximation and estimate the orbital phase. We lastly provide the possible detectability of deviations from the Kerr black hole by estimating gravitational wave dephasing and highlight the crucial role of LISA observations.

Keywords: EMRI; GW;

2023-1114

• [2311.07279] Gravitational waves from extreme-mass-ratio inspirals in the semiclassical gravity spacetime
Abstract: More recently, Fernandes discovered analytic stationary and axially-symmetric black hole solutions within semiclassical gravity, driven by the trace anomaly. The study unveils some distinctive features of these solutions. In this paper, we compute the gravitational waves emitted from the EMRI around these quantum-corrected rotating black holes using the kludge approximate method. Firstly, we derive the orbital energy, angular momentum and fundamental frequencies for orbits on the equatorial plane. We find that, for the gravitational radiation described by quadrupole formulas, the contribution from the trace anomaly only appears at higher-order terms in the energy flux when compared with the standard Kerr case. Therefore, we can compute the EMRI waveforms from the quantum-corrected rotating black hole using the Kerr fluxes. We assess the differences between the EMRI waveforms from rotating black holes with and without the trace anomaly by calculating the dephasing and mismatch. Our results demonstrate that space-borne gravitational wave detectors can distinguish the EMRI waveform from the quantum-corrected black holes with a fractional coupling constant of  within one year observation. Finally, we compute the constraint on the coupling constant using the Fisher information matrix method and find that the potential constraint on the coupling constant by LISA can be within the error in suitable scenarios

Keywords: EMRI; GW; kludge approximate method

2023-1121

• [2311.12259] Analytical models of supermassive black holes in galaxies surrounded by dark matter halos
Abstract: In this Letter, three analytical models are constructed in closed forms, each representing a supermassive black hole (SMBH) located at the center of a galaxy surrounded by a dark matter halo.The latter is modeled by the Einstein cloud. The density profile of the halo vanishes inside two Schwarzschild radii of the SMBH and satisfies the weak, strong and dominant energy conditions.The spacetime is asymptotically flat, and the difference among the three models lies in the slopes of the density profiles in the far region from the galaxy center.

Keywords: dark matter; BH

2023-1128

• [2311.15532] Detecting the tidal heating with the generic extreme-mass-ratio inspirals
Abstract: The horizon of a classical black hole, functioning as a one-way membrane, plays a vital role in the dynamic evolution of binary objects, capable of absorbing fluxes entirely. Tidal heating, stemming from this phenomenon, exerts a notable influence on the production of gravitational waves (GWs).This impact can be utilized for model-independent investigations into the nature of massive objects. In this paper, assuming that the extreme-mass-ratio inspiral (EMRI) contains a stellar-mass compact object orbiting around a massive exotic compact object (ECO) with a reflective surface, we compute the GWs from the generic EMRI orbits. Using the accurate and analytic flux formulas in the black hole spacetime, we adapted these formulas in the vicinity of the ECO surface by incorporating a reflectivity parameter. Under the adiabatic approximation, we can evolve the orbital parameters and compute the EMRI waveforms. The effect of tidal heating for the spinning and non-spinning objects can be used to constrain the reflectivity of the surface at the level of O(10^-4) by computing the mismatch and Fisher information matrix.

Keywords: EMRI; tidal heating

• [2311.16000] Bifurcation diagrams for spacetime singularities and black holes
Abstract: We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully nonlinear and dispersive nature of the underlying equations. We introduce and thoroughly explore the concept of versal unfolding (topological normal form) within the framework of the Newman-Penrose-Raychaudhuri system, the convergence-vorticity equations (notably the first and third Sachs optical equations), and the Oppenheimer-Snyder equation governing exactly spherical collapse. The findings lead to a novel dynamical depiction of spacetime singularities and black holes, exposing their continuous transformations into new topological configurations guided by the bifurcation diagrams associated with these problems.

Keywords: Singularity; black hole

• [2311.15295] Gravitational wave fluxes on generic orbits in Kerr spacetime: higher spin and large eccentricity
Abstract: To obtain the waveform template of gravitational waves (GWs), substantial computational resources and exceedingly high precision are often required. In the previous study [JCAP 11 (2023) 070], we efficiently and accurately calculate GW fluxes of a particle in circular orbits around a Schwarzschild black hole using the confluent Heun function. We extend the previous method to calculate the asymptotic GW fluxes from a particle in generic orbits around a Kerr black hole. Especially when dealing with the computational difficulties in large eccentricity e=0.9, higher spin a=0.999, higher harmonic modes and strong-field regions, our results are much better than the high-order post-Newtonian results and comparable to the results of the Mano-Suzuki-Takasugi method. Using the grid data of the asymptotic GW fluxes, we give the adiabatic waveform of non-rotating black holes, which agrees well with the waveforms of numerical relativity.

Keywords: EMRI; GW