We study the thermodynamic stability of the Kerr-AdS black hole from the perturbative corrections to the gravitational partition function. The line of critical stability is identified by the appearance of a negative mode of the Euclidean action that renders the partition function ill-defined. The eigenvalue problem, consisting of a system of three coupled partial differential equations for the metric perturbations, is solved numerically. The agreement with the standard condition of thermodynamic stability in the grand canonical ensemble is remarkable. The results illustrate the physical significance of gravitational partition functions for rotating spacetimes beyond the instanton approximation.
本文研究了具有等角动量的Kerr-AdS_5 × S^5时空的引力微扰。在这个时空中，我们发现了两种经典不稳定性，超辐射不稳定性和Gregory-Laflamme不稳定性。超辐射不稳定性是由超辐射引起的波放大和由于AdS时空的势垒引起的波反射引起的。格雷戈里-拉弗拉姆不稳定性出现在内部空间S^5的卡鲁扎-克莱因模中，破坏了对称性SO（6）。考虑到这些不稳定性，我们揭示了Kerr-AdS_5 x S^5时空的相结构。AdS/CFT对应的含义进行了讨论。
It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a BTZ black hole (BH). To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirror-like cavity or in AdS space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet boundary conditions …
We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of axisymmetric black holes proposed by Konoplya, Rezzolla and Zhidenko. In addition to its mass $M$ and specific angular momentum $a$, the black hole depends on a third parameter $η$, called the deformation parameter. We investigate how the deformation parameter affects the quasinormal modes and the quasibound states of a massive scalar field around the black hole. In pa…
The standard Black Holes (BHs) in General Relativity, as well as other ultra-compact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axi-symmetric spacetimes, non-planar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poinca…
The duality relating the four-dimensional Kerr-Taub-NUT black hole to a thermal two-dimensional CFT with central charges $c_L=c_R=12 J_0$ is analyzed in detail, generalizing an argument given recently for Kerr within the soft-hair approach. The hidden conformal symmetry is realized in the form of $Vir_L \times Vir_R$ diffeomorphisms which act non-trivially on the black hole horizon. Semiclassical formulae are derived for the temperature and central charges of the dual CFT. Assuming the applicability of the Cardy formula, these CFT quantities precisely reproduce the macroscopic Bekenstein-Hawki…
Ringed accretion disks (RADs) are agglomerations of perfect-fluid tori orbiting around a single central attractor that could arise during complex matter inflows in active galactic nuclei. We focus our analysis to axi-symmetric accretion tori orbiting in the equatorial plane of a supermassive Kerr black hole; equilibrium configurations, possible instabilities, and evolutionary sequences of RADs were discussed in our previous works. In the present work we discuss special instabilities related to open equipotential surfaces governing the material funnels emerging at various regions of the RADs, b…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce catastrophic instabilities and classic solutions become unstable under small perturbations or their evolutions. In this paper we discuss validity of the semiclassical gravity from the perspective of the spacetime instabilities and consider cosmological dynamics of the Universe in this theory. We clearly show that the homogenous and isotropic flat Universe is …
In this paper, we provide an elementary, unified treatment of two distinct blue-shift instabilities for the scalar wave equation on a fixed Kerr black hole background: the celebrated blue-shift at the Cauchy horizon (familiar from the strong cosmic censorship conjecture) and the time-reversed red-shift at the event horizon (relevant in classical scattering theory). Our first theorem concerns the latter and constructs solutions to the wave equation on Kerr spacetimes such that the radiation field along the future event horizon vanishes and the radiation field along future null infinity decays a…
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, $f(R)$-gravity, $f(T)$-gravity, string inspired black holes and brane-world cosmology. Evaporating and antievaporating black holes seem to have completely different thermodynamical features compared to standard semiclassical black holes. The purpose of this review is to provide an introduction to conceptual and technical aspects of (anti)evaporation …
In this paper, by applying the deformed dispersion relation in quantum gravity theory, we study the correction of fermions' tunneling radiation from non-stationary symmetric black holes. Firstly, the motion equation of fermions is modified in the gravitational spacetime. Based on the motion equation, the modified Hamilton-Jacobi equation has been obtained by a semiclassical approximation method. Then, the tunneling behavior of fermions at the event horizon of non-stationary symmetric Kerr black hole is investigated. Finally, the results show that in the non-stationary symmetric background, the…
Quantum-Corrected Hawking Radiation from Near-Extremal Kerr-Newman Black Holes
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；University of Science and Technology of China（中国科学技术大学）；University of Michigan（密歇根大学）；The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆理论物理国际中心）
We analyze the possibility that several instability points may be formed, due to the Paczyński mechanism of violation of mechanical equilibrium, in the orbiting matter around a supermassive Kerr black hole. We consider recently proposed model of ringed accretion disk, made up by several tori (rings) which can be corotating or counterrotating relative to the Kerr attractor due to the history of the accretion process. Each torus is governed by the general relativistic hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. We prove that the number of the instabilit…
The semiclassical stability of de Sitter spacetime
de Sitter时空和Bunch-Davies真空是描述时空几何演化的半经典爱因斯坦-薛定谔方程和具有任意曲率耦合的大质量标量量子场的解。通过计算de Sitter - Bunch-Davies系统的小空间均匀偏差的重整化能量动量张量期望值和求解线性化反反应问题，证明了该解的稳定性。重正化方案的开发。所有的动量积分都是解析地进行的。根据拉普拉斯变换给出了一般解。它只包含两个人为的不稳定性：一个恒定的规范模式和普朗克时间尺度上的不稳定性躺在我们的半经典理论的范围之外。
Nonlinear electroweak sphaleron clouds around Kerr black holes
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用数学研究与发展中心）；Universität Oldenburg（奥尔登堡大学）；U. Federal do Pará（帕拉联邦大学）
In this work we analyse the potential for a warp drive spacetime to develop instabilities due to the presence of quantum matter. Particularly, we look for points of infinite blueshift (which are analogous to points of a black hole inner horizon, known for its semiclassical instability), and categorise them through the behaviour of geodesics in their vicinity. We find that warp-drive bubbles in dimension 2+1 or higher are in fact likely to be stable, as they generally contain only isolated points where divergences are approached, leading to a finite limit for the overall accumulation of destabi…
A large portion of the studies concerning the quasinormal mode frequencies of a Kerr black hole have focused only on achieving higher numerical accuracy with limited emphasis on providing their physical interpretation. In this article, we partially address this issue by computing the quasinormal mode frequency spectrum of a Kerr black hole using the theory of Regge poles. By considering the retarded Green's function of the Teukolsky equation, we establish for scalar, electromagnetic and gravitational perturbations an equation linking the Regge poles to the quasinormal frequencies and we solve …
The wave equation $\square_{g_{M,a}}ψ=0$ on subextremal Kerr spacetimes $(\mathcal{M}_{M,a},g_{M,a})$, $0<|a|<M$, does not admit real mode solutions, as was established by Shlapentokh-Rothman. In this paper, we show that the absence of real modes does not persist under the addition of an arbitrary short-range non-negative potential $V$ to the wave equation or under changes of the metric $g_{M,a}$ in the far away region of $\mathcal{M}_{M,a}$ (retaining the causality of $T$ there). In particular, we first establish, for any $0<|a|<M$, the existence of real mode solutions $ψ$ to equation $\squar…
Large, localized variations of light scalar fields tend to collapse into black holes, dynamically "censoring" distant points in field space. We show that in some cases, large scalar excursions in asymptotically flat spacetimes can be UV-completed by smooth Kaluza-Klein bubble geometries, appearing to circumvent 4d censorship arguments. However, these spacetimes also exhibit classical instabilities related to the collapse or expansion of a bubble of nothing, providing a different censorship mechanism. We show that the Kerr family of static KK bubbles, which gives rise to an infinite scalar excu…
Quantum field effects on a classical background spacetime may be obtained from the semiclassical equations of General Relativity with the expectation value of the stress-energy tensor of the quantum field as a source. This expectation value can be calculated from Hadamard's elementary two-point function, which in practice is given in terms of sums of products of field modes evaluated at two spacetime points. We derive expressions for the two-point function for a massless scalar field in the Unruh state on a Kerr black hole spacetime. Our main result in this paper is a novel expression valid wh…
Charged rotating Kerr-Newman black holes are known to be superradiantly unstable to perturbations of charged massive bosonic fields whose proper frequencies lie in the bounded regime $0 < ω< \text{min} \{ω_{\text{c}} \equiv m Ω_{\text{H}} + qΦ_{\text{H}},μ\}$ [here $\{Ω_{\text{H}}, Φ_{\text{H}}\}$ are respectively the angular velocity and electric potential of the Kerr-Newman black hole, and $\{m,q,μ\}$ are respectively the azimuthal harmonic index, the charge coupling constant, and the proper mass of the field]. In this paper we study analytically the complex resonance spectrum which characte…
A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological consta…
