The general parametrization of a black-hole spacetime in arbitrary metric theories of gravity includes an infinite set of parameters. It is natural to suppose that essential astrophysically observable quantities, such as quasinormal modes, parameters of shadow, electromagnetic radiation and accreting matter in the vicinity of a black hole, must depend mostly on a few of these parameters. Starting from the parametrization for spherically symmetric configurations in the form of infinite continued fraction, we suggest a compact representation of the asymptotically flat spherically symmetric and slowly rotating black holes in terms of only three and four parameters respectively. A subclass of arbitrarily rotating black holes belonging to the Carter family can also be parametrized by only four parameters. This approximate representation of a black-hole metric should allow one to describe physical observables in the region of strong gravity.
Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional …
X-ray reflection spectroscopy is a promising technique for testing general relativity in the strong field regime, as it can be used to test the Kerr black hole hypothesis. In this context, the parametrically deformed black hole metrics proposed by Konoplya, Rezzolla \& Zhidenko (Phys. Rev. D93, 064015, 2016) form an important class of non-Kerr black holes. We implement this class of black hole metrics in \textsc{relxill\_nk}, which is a framework we have developed for testing for non-Kerr black holes using X-ray reflection spectroscopy. We perform a qualitative analysis of the effect of the le…
Kerr-referenced analytical parametrization of rotating black holes in dynamical Chern-Simons gravity
New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent State Technical University（塔什干国立技术大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）
The general parametrization of spherically symmetric and asymptotically flat black-hole spacetimes in arbitrary metric theories of gravity was suggested in [3]. The parametrization is based on the continued fraction expansion in terms of the compact radial coordinate and has superior convergence and strict hierarchy of parameters. It is known that some observable quantities, related to particle motion around the black hole, such as the eikonal quasinormal modes, radius of the shadow, frequency at the innermost stable circular orbit, and others, depend mostly on only a few of the lowest coeffic…
Black hole thermodynamics has brought strong hints of a profound and fundamental connection between gravity, thermodynamics, and quantum theory. If the black hole does behave like a natural thermodynamic system, it should be thermodynamically stable in a clean environment. In this paper, using the observational data of binary black hole (BBH) mergers observed by LIGO, Virgo, and KAGRA detectors, we check whether the black hole remnants produced from BBH mergers in the LIGO-Virgo-KAGRA catalog GWTC-3 are thermodynamically stable. The criterion for the thermodynamic stability is quite simple and…
Black hole photon ring beyond General Relativity: an integrable parametrization
Arnold Sommerfeld Center for Theoretical Physics（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Sciences and Technology（慕尼黑量子科学与技术中心）；Université de Lyon, ENS de Lyon, Laboratoire de Physique, CNRS UMR 5672（里昂大学，巴黎高等师范学院里昂分校，物理实验室，法国国家科学研究中心）；LUX, CNRS UMR 8262, Observatoire de Paris - PSL, Sorbonne Université Paris（卢克瑟姆天文台，法国国家科学研究中心，巴黎天文台-巴黎文理研究大学，索邦巴黎大学）；Laboratoire de Mathématiques de Bretagne Atlantique, CNRS UMR 6205, Université de Bretagne Occidental（布列塔尼大西洋数学实验室，法国国家科学研究中心，布列塔尼西部大学）
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
Gravitational-wave detections of black hole mergers in binary systems offer an excellent opportunity to test the 2nd law of black hole thermodynamics. In this paper, we review how the entropy of any astrophysical black hole is calculated and we use LIGO and VIRGO's mass and spin data measurements from black hole merger events detected over the past years to perform entropy calculations and numerically test the generalized 2nd law of thermodynamics. Besides, we analyze the mathematical correlation between the black hole merger event's initial parameters to prove and conclude that the theorem wi…
We extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evapo…
We investigate scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields inspired by the $N=4$ supergravity. From the onset of the spontaneous scalarization (tachyonic instability of Reissner-Nordström black hole), these black holes are classified by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes. Adopting radial perturbations, we show that the $n=0$ black hole is stable against the $s(l=0)$-mode scalar perturbation, whereas the $n=1,2$ excited black holes are unstable. This …
We construct spontaneously vectorized black holes where a real vector field is coupled to the Gauss-Bonnet invariant. We employ three coupling functions for the vector field, and determine the respective domains of existence of the vectorized black holes. These domains of existence are bounded by the marginally stable Schwarzschild black holes and the critical vectorized black holes. We also address the effects of a mass term. For a given black hole mass the horizon radius is smaller for the vectorized black holes than for the Schwarzschild black holes. Since the vector field vanishes at the h…
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the …
In General Relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to lowest order in spin, as the metrics of stellar objects; (ii) they are independent of mass, when expressed in geometric units; and (iii) they are described by the Kerr metric. In this paper, we quantify the upper bounds on potential black-hole metric deviations imposed by observations of black-hole shadows and of binary black-hole inspirals in order to explore the current experimental limits on possible violations of the last two predictions. We find that both types of experiments …
It was confirmed that the negative modes of the Euclidean section for asymptotically flat black holes reveal the thermodynamic instability of these black holes in the grand canonical ensemble (GCE). These include Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes. In this work, we develop the relation between thermodynamic instability in the GCE and tachyonic instability for asymptotically flat black holes, where the latter is the onset for obtaining black holes with scalar hair. This implies that the tachyonic instability of black holes when introducing scalar coupling to th…
A population of more than 50 binary black hole mergers has now been observed by the LIGO and Virgo gravitational-wave observatories. While neutron stars are known to have large velocities associated with impulsive kicks imparted to them at birth in supernovae, whether black holes receive similar kicks, and of what magnitude, remains an open question. Recently, Callister et al. (2021) analysed the binary black hole population under the hypothesis that they were all formed through isolated binary evolution and claimed that large black hole kicks (greater than 260 km/s at 99% confidence) were req…
