On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

We review the topic of 4D Einstein–Gauss–Bonnet (4DEGB) gravity, which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock’s theorem, and the subject of Gauss–Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss–Bonnet term in four space–time dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4DEGB gravity exhibits a number of interesting phenomena in each of these areas.

The 4D Einstein–Gauss–Bonnet theory of gravity: a review

We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordstrom (RN) and Kerr black holes in a unified way. An advantage of the AIM over the standard continued fraction method (CFM) is that for differential equations with more than three regular singular points Gaussian eliminations are not required. However, the convergence of the AIM depends on the location of the radial or angular position, choosing the best such position in general remains an open problem. This review presents for the first time the spin 0, 1/2 & 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM, and confirms results previously obtained using the CFM. We also presents some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher dimensional generalizations and we give an example of doubly rotating black holes.

A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method

We obtain the Page curves of an eternal Reissner-Nordstr\"om black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general ${\cal O}(R^2)$ terms plus Maxwell term and Einstein-Gauss-Bonnet gravity plus Maxwell term. In both the cases entanglement entropy of the Hawking radiation in the absence of island surface is increasing linearly with time. After including contribution from the island surface, we find that after the Page time, entanglement entropy of the Hawking radiation in both the cases reaches a constant value which is the twice of the Bekenstein-Hawking entropy of the black hole and we obtain the Page curves. We find that Page curves appear at later or earlier time when the Gauss-Bonnet coupling increases or decreases. Further, scrambling time of Reissner-Nordstr\"om is increasing or decreasing depending upon whether the correction term (coming from ${\cal O}(R^2)$ terms in the gravitational action) is increasing or decreasing in the first case whereas scrambling time remains unaffected in the second case (Einstein-Gauss-Bonnet gravity case). As a consistency check, in the limit of vanishing GB coupling we obtain the Page curve of the Reissner-Nordstr\"om black hole obtained in arXiv:2101.06867. 

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Page curves of Reissner–Nordström black hole in HD gravity

In this paper, we explore three simple models of accretions on a global monopole black hole in f(R) theory, and numerically study the corresponding observational appearances as seen by an observer located at the asymptotic infinity and the certain region out of black hole. For the thin-disk accretion, the results here show that the brighter lensing ring and the darker photon ring that around black hole shadow, always make a small contribution and a negligible contribution to total observed intensity respectively. While, the direct emission of disk contributes a dominant part, and the size of shadow always depends on the disk’s location. For the static and infalling spherical accretions, it turns out that the radiuses of the shadows and photon spheres are always same for both accretions, which implies that the boundary of shadow represents the signature of the spacetime geometry in this case. However, we also find that the brightness of shadow in infalling accretion is darker than that in static case since the Doppler effect is taken into account. In addition, the effect of the global monopole parameter $$\eta $$
 and f(R) parameter $$\psi _0$$
 on observational appearances of black hole are clearly emphasized throughout of this paper. Finally, we conclude that black hole shadows and the related rings with some different observable features can be used for us to distinguish black holes from different gravity theories and set the upper limits to the f(R) parameter $$\psi _0$$
 .

Observational appearances of a f(R) global monopole black hole illuminated by various accretions

https://doi.org/10.1016/j.physletb.2022.137343

Chaos bound and its violation in charged Kiselev black hole


 In this paper, we investigate the influence of the angular momentum of a charged particle around non-extremal and extremal Einstein-Maxwell-Dilaton-Axion black holes on the Lyapunov exponent. The angular momentum's ranges and spatial regions where the bound of the exponent is violated are found for certain values of the rotation parameter and dilatonic constant of the black holes. This violation always exists when the rotation parameter is large enough and the rotation directions of the particle is opposite to those of the black holes. The spatial regions outside the extermal black hole for the violation is relatively large. In the near-horizon regions of the extremal black holes, the violation depends on the rotation directions of the black holes and particle, and does not depend on the value of the angular momentum.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

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Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes

In this paper, we investigate influences of the charge and angular momentum of a particle around a charged Einstein–Euler–Heisenberg AdS black hole on a Lyapunov exponent, and find spatial regions where the chaos bound is violated. Positions of circular orbits are gotten by fixing the charge and angular momentum of the particle, respectively. The positions gradually move away from the event horizon with the increase of the angular momentum when the charge is fixed and with the decrease of the charge when the angular momentum is fixed. For certain values of the charge, angular momentum and Euler–Heisenberg parameter, the spatial regions where the bound is violated are found. When the charge is fixed and the Euler–Heisenberg parameter is large, a small angular momentum causes the violation. Although the angular momentum is small, the corresponding spatial region is not small. An interesting discovery is that the bound is violated by the black hole when the particle’s charge is less than 1 and Λ=0 , but this requires the black hole’s charge to be large enough. This violation may be related to the dynamical stability of the black hole. The backreaction of the particle on the background spacetime is not considered in the investigation.

Angular momentum and chaos bound of charged particles around Einstein–Euler–Heisenberg AdS black holes

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein–Gauss–Bonnet black hole. The perturbation of a massless scalar field in the black hole’s background is adopted. The quasinormal modes are gotten by the 6th order WKB approximation approach and shadow radius, respectively. When the value of the Gauss–Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss–Bonnet coupling constant and multipole number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein–Gauss–Bonnet–Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss–Bonnet coupling constant.

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The correspondence between shadow and test field in a four-dimensional charged Einstein–Gauss–Bonnet black hole

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black hole's background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss-Bonnet coupling constant and multiple number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein-Gauss-Bonnet-Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss-Bonnet coupling constant.

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Chuanhong Gao

Papers

Chaos bound and its violation in charged Kiselev black hole

Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes

Angular momentum and chaos bound of charged particles around Einstein–Euler–Heisenberg AdS black holes

The correspondence between shadow and test field in a four-dimensional charged Einstein–Gauss–Bonnet black hole

The correspondence between shadow and test field in a four-dimensional charged Einstein-Gauss-Bonnet black hole