Sitter Black Hole Research Articles

Quasinormal modes and isospectrality of Bardeen (Anti-) de Sitter black holes* *Supported by the the Natural Science Foundation of Hunan Province, China (2022JJ40262), and the National Natural Science Foundation of China (12375046, 12205254)

Black holes (BHs) exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who considered the Einstein equation coupled with a nonlinear electromagnetic field. In this study, we investigate the gravitational perturbations, including the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes (QNMs) through numerical methods. For the Bardeen de Sitter black hole, we employ the 6th-order WKB approach. The numerical results reveal that the isospectrality is broken in this case. Conversely, the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.

Quasilinear wave equations on Schwarzschild–de Sitter

We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild–de Sitter black hole backgrounds, for appropriately small initial data. The core of the argument is entirely local, based on time translation invariant energy estimates in spacetime slabs of fixed time length. Global existence then follows simply by iterating this local result in consecutive spacetime slabs. We infer that an appropriate future energy flux decays exponentially with respect to the energy flux of the initial data.

P-v criticality of charged Reissner–Nordström-de Sitter black hole under the influence of Lorentz violation theory

In this paper, the modified Hawking radiation and the P-v criticality of Reissner–Nordström-de Sitter (RNdS) black hole are investigated by using Dirac equation with Lorentz violation theory in curved space–time. Taking cosmological constant as the thermodynamic pressure and its conjugate quantity as thermodynamic volume, the analogy between the RNdS black hole in the ensemble with fixed charge and van der Waals liquid-gas system is derived. We also study the equation of state, critical exponents, critical point, heat capacity, entropy correction, Gibbs free energy. It is worth mentioning that the critical temperature, entropy, Gibbs free energy and Helmholtz free energy are modified but the critical exponents are found to be unchanged due to the influence of Lorentz violation theory. We observe that the number of Hawking–Page critical point increases due to Lorentz violation theory.

Overcharging an accelerating Reissner-Nordström-anti-de Sitter black hole with test field and particle

Accelerating black holes have been widely studied in the context of black hole thermodynamics, holographic gravity theories, and in the description of black holes at the center of galaxies. As a fundamental assumption to ensure spacetime causality, we investigate the weak cosmic censorship conjecture (WCCC) in the accelerating Reissner-Nordström-Anti-de Sitter (RN-AdS) spacetime through the scattering of a charged field and the absorption of a charged particle. For the scattering of a charged scalar field, both near-extremal and extremal accelerating RN-AdS black holes cannot be overcharged, thereby upholding the validity of the WCCC. In the case of the absorption of a test charged particle, the results demonstrate that the event horizon of the extremal accelerating RN-AdS black hole cannot be destroyed, while the event horizon of the near-extremal black hole can be overcharged if the test particle satisfies certain conditions. The above results suggest that, in the case of test particles, second-order effects like self-force and self-energy should be further considered.

Ruppeiner geometry and the fluctuation of the RN-AdS black hole in framework of the extensive thermodynamics

In this study, the Ruppeiner geometry and fluctuations of a four-dimensional charged Anti-de Sitter (AdS) black hole within the context of extensive thermodynamics have been investigated. By fixing the AdS radius in Vissers' construction, an extensive thermodynamics description of the RN-AdS black hole is established, with the central charge playing the role of the particle number, introducing the concept of a subsystem into black hole thermodynamics. By employing the density of thermodynamic variables, the phase transition of the black hole is reexamined, and this result holds for black holes with different AdS backgrounds. Furthermore, the authors delve into a detailed analysis of the Ruppeiner geometry using fluctuation theory. Interestingly, an increase in the particle number of the smaller subsystem is found to induce a reduction in the thermodynamic curvature scalar.

P − v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics

Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) black holes has been shown to exhibit physically interesting features, such as P − V criticalities and van der Waals-like phase transitions. In this work we extend the study of these critical phenomena to Kaniadakis theory, which is a non-extensive generalization of the classical statistical mechanics incorporating relativity. By applying the typical framework of condensed-matter physics, we analyze the impact of Kaniadakis entropy onto the equation of state, the Gibbs free energy and the critical exponents of AdS black holes in the extended phase space. Additionally, we investigate the underlying micro-structure of black holes in Ruppeiner geometry, which reveals appreciable deviations of the nature of the particle interactions from the standard behavior. Our analysis opens up new perspectives on the understanding of black hole thermodynamics in a relativistic statistical framework, highlighting the role of non-extensive corrections in the AdS black holes/van der Waals fluids dual picture.

Restoring strong cosmic censorship in Reissner–Nordström–de Sitter black holes via non-minimal electromagnetic-scalar couplings

We investigate whether the Strong Cosmic Censorship (SCC) Conjecture can be reinstated at the classical level in Reissner–Nordström–de Sitter (RNdS) black holes by introducing non-minimal couplings between the electromagnetic and scalar fields in Einstein–Maxwell-scalar (EMS) theory. By conducting numerical calculations, we find that the SCC can be restored within a specific range of the coupling constant. Notably, for a given value of the cosmological constant, there exists a critical coupling constant above which the EMS theory satisfies the SCC. These findings suggest that the non-minimal couplings between the electromagnetic and scalar fields may play a crucial role in the restoration of the SCC in RNdS spacetime. Additionally, under negative coupling constants, the low-lying modes of nearly extremal black holes exhibit β>1,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta > 1,$$\\end{document} enabling C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^2$$\\end{document} extensions beyond the Cauchy horizon and intensifying the violation of the SCC.

Entropy Bounds for Rotating AdS Black Holes.

We propose novel thermodynamic inequalities that apply to stationary asymptotically anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favor. Intriguingly, our findings indicate that these inequalities may also apply for black holes of nonspherical horizon topology, as we show their validity as well for thin asymptotically AdS black rings.

Heat engines of the Kerr-AdS black hole

In this paper, we investigate three types of heat engines for the rotating Kerr-Anti de Sitter (Kerr-AdS) black hole. We first briefly review the thermodynamics and phase structure of the Kerr-AdS black hole and obtain the phase structure in the T–S chart. The thermal stability of Kerr-AdS black holes, along with their dependence on various parameters, is thoroughly examined. Then, by utilizing the phase diagram, we consider three types of heat engines: the maximal Carnot engine, Stirling engine, and Rankine engine. We calculate both the work and efficiency for these engines. The results indicate that angular momentum has a significant influence on these heat engines.

Impact of quintessence and cloud of strings on self-consistent d-dimensional charged thin-shell wormholes

This article evaluates the stability constraints of higher-dimensional geometry of thin-shell wormholes developed from the two equivalent copies of inner and outer d-dimensional charged anti-de Sitter black holes bounded by a cloud of strings and quintessence. Such geometrical structures are built using a cut-and-paste method that joins two identical forms of black hole solutions at the hypersurface. We develop the equation of motion for the constructed wormholes and then use the linear radial perturbation approach to examine the stable configuration. The stability constraints depend on the dimensions of the black holes, cloud, and quintessence parameters. It is worth mentioning that the possibility of a stable structure is greatest for the choice of d-dimensional charged anti-de Sitter black holes with quintessence and a cloud of strings.

Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond

Abstract Although the WKB series converges only asymptotically and guarantees the exact result solely in the eikonal regime, we have managed to derive concise analytical expressions for the quasinormal modes and grey-body factors of black holes, expanding beyond the eikonal approximation. Remarkably, these expressions demonstrate unexpectedly strong accuracy. We suggest a comprehensive approach for deriving analytical expressions for grey-body factors and quasinormal modes at various orders beyond the eikonal approximation. Two cases are examined as examples: the Schwarzschild-de Sitter black hole and hairy black holes within the framework of Effective Field Theory. We have publicly shared a generic code that calculates analytical expressions for grey-body factors and quasinormal modes of spherical black holes.

Thermal fluctuations, QNMs, and emission energy of charged ADS black hole with nonlinear electrodynamics

This study examines the thermodynamics of charged anti-de Sitter (AdS) black holes (BHs) with nonlinear electrodynamics (NED) using quasinormal modes (QNMs) and thermal fluctuations. For this purpose, we calculate the Hawking temperature and discuss the stable configuration of the considered black hole using heat capacity. First, we study the interesting aspects of the emission of energy. Then, we explore the effects of thermal corrections on thermodynamic quantities and their corrected energies. We study the phase transitions of the system in the background of thermal fluctuations. It is concluded that the presence of a coupling constant enhances the thermodynamically stable configuration of uncharged and charged AdS BH geometries. We highlight that our results are in good agreement with the thermodynamics of the previous black hole solutions and assumptions presented in the literature.

AdS Black Hole Thermodynamics and Microstructures from f(Q)$f(Q)$ Gravitation

AbstractThe significant properties and phase transition of charged Anti‐de Sitter (AdS) black holes have been extensively studied in a variety of modified theories of gravity in the presence of numerous matter fields. The goal of the current research is to investigate the AdS black hole's thermodynamics under the impact of gravity. Additionally, this paper explores the black hole's local stability and phase structure under the relevant gravity. Besides, Ruppeiner geometry is used to look into the AdS black hole's microscopic structure. The Ricci curvature scalar R to explain the interactions between the AdS black hole's microscopic particles under the influence of gravity have been numerically computed.

Time evolution of Einstein-Maxwell-scalar black holes after a thermal quench

We employ the holographic quench technique to drive Einstein-Maxwell-scalar (EMs) black holes out of equilibrium and study the real-time dynamics therein. From the fully nonlinear dynamical simulations, a dynamically unstable Reissner-Nordström anti-de Sitter (RN-AdS) black hole can be scalarized spontaneously after an arbitrarily small quench. On the other hand, a dynamically stable scalarized black hole can be descalarized after a quench of sufficient strength. Interestingly, on the way to descalarization, the scalarized black hole behaves like a holographic superfluid, undergoing a dynamical transition from oscillatory to non-oscillatory decay. Such behaviors are related to the spectrums of quasi-normal modes of scalarized black holes, where the dominant mode migrates toward the imaginary axis with increasing quench strength. In addition, due to the ℤ2-symmetry preserved by the model, the ground state is degenerate. We find that there exists a threshold for the quench strength that induces a dynamical transition of the gravitational system from one degenerate ground state to the other. Near the threshold, the gravitational system is attracted to an excited state, that is, a RN-AdS black hole with dynamical instability.

Quasinormal modes of phantom Reissner-Nordström-de Sitter black holes

In this paper, we investigate some characteristics of phantom Reissner-Nordström-de Sitter (RN-dS) black holes. The peculiar features of phantom field render this kind of black holes quite different from their counterparts. We can only find at most two horizons in this spacetime, i.e. event horizon and cosmological horizon. For the black hole charge parameter, we find that it is not bounded from below. We calculate quasinormal modes (QNMs) frequencies of massless neutral scalar field perturbation in this black hole spacetime, and some properties related to the large charge parameter are disclosed.

Thermodynamics, Ruppeiner geometry, and topology of Born-Infeld black hole in asymptotic flat spacetime

In the extended phase space, Born-Infeld anti-de Sitter black holes exhibit diverse phase transitions including the van der Waals type and reentrant phase transitions. In this paper, we aim to investigate the potential thermodynamical features for Born-Infeld black holes when the cosmological constant vanishes. Quite differently, although there present the swallow tail behavior of the free energy and temperature-entropy criticality, no phase transition will occur when we consider the thermodynamical stability. Further, based on these findings, the phase structures are explicitly shown with the stable, unstable black hole, and non-black hole regions. After excluding the non-black hole region, we observe that the scalar curvature of the Ruppeiner geometry is always positive, indicating a dominant repulsive interaction for both the stable and unstable black holes. Particularly, we also establish the topology for the thermodynamical critical point. By calculating the topological number, we confirm that this critical point of the Born-Infeld black holes is a conventional one. Although it is not an indicator of the first small-large black hole phase transition, it does signify the emergence of stable intermediate black holes. All these results uncover the thermodynamical features of the Born-Infeld black holes in the absence of the cosmological constant.

Phase structure of quantum improved Schwarzschild-(Anti)de Sitter black holes

We study the phase structure of quantum improved Schwarzschild–(A)dS black holes in asymptotically safe gravity. Our results confirm some of the well-known properties of quantum black holes. For example, the quantum effect provides a repulsive force in the core region near singularity which stabilizes the thermodynamically unstable small black holes, and also creates a zero temperature state with finite size. We suggest that this could be a candidate for dark matter. We find a new second order phase transition between small and large black holes for quantum improved Schwarzschild-Anti de Sitter black holes. We also discuss the black holes with different spatial topologies and find a notable duality.

A quantum analog model for a scalar particle interacting with a Kerr–de Sitter black hole

We study the thin-layer quantization of a Schrödinger particle constrained to move along an oblate spheroidal surface embedded in Euclidean space as an analog model to a particle in the background of a black hole and of a wormhole. The Schrödinger equation for the superficial wavefunction leads to an ordinary differential equation with five singularities — four regular and one irregular. We manage to transform this equation into a generalized Heun’s equation, with three regular singular points and one irregular singularity at infinity. This equation was studied by Schäfke and Schmidt back in 1980. By means of an external potential, we are able to reproduce the equations of motion of a particle close both to a black hole and a wormhole, thus creating an effective analog model. Additionally, we present correct and exact solutions for the radial part of the Klein–Gordon equation in the Kerr–de Sitter metric.

Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes’ parameters. Since k and c_ 0^2c_2 m^2 appear together in the generalized free energy in the form of k +c_ 0^2c_2 m^2 , where k characterizes the horizon curvature and c_2 m^2 is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

Time like geodesics for five-dimensional Schwarzschild and Reissner–Nordström anti-de Sitter black holes

The time like structure of the five-dimensional Schwarzschild and Reissner–Nordström anti-de Sitter black holes is studied in detail. Different kinds of motion are allowed and studied by using an adequate effective potential. Then, by solving the corresponding equations of motion, several trajectories and orbits are described in terms of Weierstraß elliptic functions and elementary functions for neutral particles.