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The island rule for the entanglement entropy is applied to an eternal Reissner-Nordstr\"om black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes., Comment: 20 pages, 4 figures, references and comments added

We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr black holes. We show that WENO methods outperform higher-order finite-difference methods, standard in the discretization of the Teukolsky equation, due to the need to add dissipation for stability purposes in the latter. In particular, as the WENO scheme uses no additional dissipation, it is well suited for scenarios requiring long-time evolution such as the study of price tails and gravitational wave emission from extreme mass ratio binaries. In the mixed-precision approach, the expensive computation of the WENO weights is performed in reduced floating-point precision that results in a significant speedup factor of $$\approx 3.3$$ . In addition, we use state-of-the-art Nvidia general-purpose graphics processing units and cluster parallelism to further accelerate the WENO computations. Our optimized WENO solver can be used to quickly generate accurate results of significance in the field of black hole and gravitational wave physics. We apply our solver to study the behavior of the Aretakis charge—a conserved quantity, that if detected by a gravitational wave observatory like LIGO/Virgo would prove the existence of extremal black holes.

The recently obtained hairy Kerr black holes, due to additional sources or surrounding fluid, like dark matter, with conserved energy-momentum tensor, have a deviation $\alpha$ and primary hair $l_0$, apart from rotation parameter $a$ and mass $M$. In the wake of the \textit{Event Horizon Telescope} (\textit{EHT}) observations of the supermassive black hole M87*, a recent surge in interest in black hole shadows suggests comparing the black holes in general relativity (GR) and modified theories of gravity (MoG) to assess these models' differences. Motivated by this, we take on an extensive study of the rotating hairy Kerr black holes, which encompasses, in particular cases, the Kerr black hole ($\alpha=0$). We investigate ergosphere and shadows of the black holes to infer that their size and shape are affected due to the $l_0$ and are found to harbour a richer chaotic structure. In particular, the hairy Kerr black holes possess smaller size but more distorted shadows when compared with Kerr black holes. We also estimate the parameters $l_0$ and $a$ associated with hairy Kerr black holes using the shadow observables. The inferred circularity deviation $\Delta C \leq 0.1$ for the M87* black hole is satisfied, whereas shadow angular diameter $\theta_{d}=42 \pm 3 \mu as$, within $1 \sigma$ region, for a given choice of $\alpha$, places bounds on the parameters $a$ and $l_0$. Interestingly, the shadow axial ratio obeying $1< D_x \lesssim 4/3$ is in agreement with the \textit{EHT} results and thus eventuates in the hairy Kerr black holes being suitable candidates for astrophysical black holes., Comment: 15 pages, 13 figures, 2 tables. Matched to the published version

An important open question in black hole thermodynamics is about the existence of a "mass gap" between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordstr\"{o}m near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on $S^2$ in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of $2d$ Jackiw-Teitelboim gravity coupled to the electromagnetic $U(1)$ gauge field and to an $SO(3)$ gauge field generated by the dimensional reduction., Comment: 54 pp; v2 Ref added and correction regarding the relation between angular momentum and SO(3) charge

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

We study some aspects of the de Sitter version of Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, we have a boundary mode when we compute observables with a fixed dilaton and metric at the boundary. We compute the no-boundary wavefunctions and probability measures to all orders in perturbation theory. We also discuss contributions from different topologies, borrowing recent results by Saad, Shenker and Stanford. We discuss how the boundary mode leads to gravitational corrections to cosmological observables when we add matter. Finally, starting from a four dimensional gravity theory with a positive cosmological constant, we consider a nearly extremal black hole and argue that some observables are dominated by the two dimensional nearly de Sitter gravity dynamics., Comment: 66 pp, 15 figs; v2: ref added

We use N = 8 supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at O(G3) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known D-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order. © 2020, The Author(s)., Journal of High Energy Physics, 2020 (11), ISSN:1126-6708, ISSN:1029-8479

Light rings (LRs) play an important role in gravitational wave observations and black hole photographs. In this paper, we investigate general features of LRs in stationary, axisymmetric, asymptotically flat spacetimes with or without horizons. For a nonextremal black hole, we show explicitly that there always exist at least two LRs propagating in opposite directions, where the outermost one is radially unstable. For an extremal black hole, we show that there exists at least one retrograde LR. We find that there is at least one LR which is angularly stable. The stability analysis does not involve any energy condition. Our method also applies to horizonless spacetimes and we prove that LRs always appear in pairs. Only some natural and generic assumptions are used in our proof. The results are applicable to general relativity as well as most modified theories of gravity. In contrast to previous works on this issue, we obtain much stronger results with a much more straightforward approach., Comment: 6pages, 5 figures,major revision, arguments and results improved, matched version in PRD

We examine the accretion of matter onto a black hole in scalar--tensor--vector gravity (STVG) also known as modified gravity (MOG). The gravitational constant is $G=G_{N} (1 + \alpha)$ where $\alpha$ is a parameter taken to be constant for static black holes in the theory. The MOG black hole is spherically symmetric and characterised by two event horizons. The matter falling into the black hole obeys the polytrope equation of state and passes through two critical points before entering the outer horizon. We obtain analytical expressions for the mass accretion rate as well as for the outer critical point, critical velocity and critical sound speed. Our results complement existing strong field tests like lensing and orbital motion and could be used in conjunction to determine observational constraints on MOG., Comment: 6 pages, 1 figure, changed to match published version

In this work, we explore all possible scenarios in the evaporation process of a spherical neutral AdS black hole in four-dimensional conformal gravity, where the equations of states are branched. In one branch, the final states correspond to the extremal black hole where the total decay time is divergent given any initial mass. In the other branch, the black holes always evaporate completely with in a finite time; the total decay time depends linearly on the AdS radius, when the mass is taken to be infinity., Comment: 6 page+references;minor corrections, references added, accepted by PLB

Considering Hawking radiation with angular momentum, we propose a modified Stefan–Boltzmann law about the particles with both energy and angular momentum radiated from a Kerr black hole. Based on the modified Stefan–Boltzmann law, we calculate the entropy in the interior volume of the Kerr black hole and investigate the proportional relation between the variation of this entropy and the variation of Bekenstein–Hawking entropy under Hawking radiation. Comparing to Hawking radiation without angular momentum, we find that whether the particles radiated from the black hole take angular momentum cannot affect the proportional relation between the two types of entropy. Furthermore, the proportionality coefficient of the two types of entropy is investigated. It is found that this coefficient is approximately a constant except the late stage of Hawking radiation. Moreover, the proportional relation can degenerate to the Schwarzschild case when the angular momentum of the black hole completely disappears. For a Kerr black hole, the extremal black hole can technically not prevent and stop the evaporation anymore under Hawking radiation with angular momentum.

A Kaluza-Klein state configuration in black-hole qubit correspondence (BHQC) is considered in cyclic cycles of its Bekenstein-Hawking entropy. After a sequence of Peccei-Quinn transformations on the Kaluza-Klein state in cyclic cycles alternating between large and small extremal black hole (EBH) configurations, we obtain the corresponding amount of variation in the initial Bekenstein-Hawking entropy in cyclic cycles. We consider different cases where the EBH state alternates between small and large states. We then demonstrate that the total Bekenstein-Hawking entropy increases in these processes.

Under charged Hawking radiation, we calculate the entropy of the scalar field in the interior volume of a Reissner–Nordstrom (RN) black hole and investigate the proportional relation between this entropy and the Bekenstein–Hawking entropy. Comparing with uncharged Hawking radiation, we find that whether the particles radiated from the black hole are charged cannot affect the proportional relation between the two types of entropy. Furthermore, the proportionality coefficient of the two types of entropy has been analyzed and discussed. The result shows that the variation of scalar field entropy inside the black hole is approximately proportional to the variation of Bekenstein–Hawking entropy in an infinitesimal evaporation process. Moreover, the proportional relation can degenerate to the Schwarzschild case when the charge of the black hole completely disappears. For a charged black hole, the extremal black hole will technically not prevent and stop the evaporation anymore under charged Hawking radiation.

We present a new solution in Einstein-Maxwell theory which can be considered as the magnetized version of Kerr-Taub-NUT solution. Some properties of the spacetime are discussed. We also compute the entropy of extremal black hole in the spacetime by using the Kerr/CFT correspondence approach., 18 pages, 1 figure

The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is an influential solution of the low energy heterotic string theory. As it is well known, it presents a singular extremal limit. We construct a regular extension of the GMGHS extremal black hole in a model with $\mathcal{O}(\alpha')$ corrections in the action, by solving the fully non-linear equations of motion. The de-singularization is supported by the $\mathcal{O}(\alpha')$-terms. The regularised extremal GMGHS BHs are asymptotically flat, possess a regular (non-zero size) horizon of spherical topology, with an $AdS_2\times S^2$ near horizon geometry, and their entropy is proportional to the electric charge. The near horizon solution is obtained analytically and some illustrative bulk solutions are constructed numerically., Comment: 14 pages, 3 figures, Journal version