AdS Black Holes Research Articles

Quasinormal modes and stability of accelerating Reissner-Norsdtröm AdS black holes

We investigate the numerical stability of accelerating AdS black holes against linear scalar perturbations. In particular, we study the evolution of a probe non-minimally coupled scalar field on Schwarzschild and Reissner-Nordström AdS black holes with small accelerations by computing the quasinormal modes of the perturbation spectrum. We decompose the scalar field Klein-Gordon equation and study the eigenvalue problem for its angular and radial-temporal parts using different numerical methods. The angular part is written in terms of the Heun solution and expanded through the Frobenius method which turns out to give eigenvalues qualitatively similar to the ones obtained through the spherical harmonics representation. The radial-temporal evolution renders a stable field profile which is decomposed in terms of damped and purely imaginary oscillations of the quasinormal modes. We calculate the respective frequencies for different spacetime parameters showing the existence of a fine-structure in the modes, for both real and imaginary parts, which is not present in the non-accelerating AdS black holes. Our results indicate that the Schwarzschild and Reissner-Nordström AdS black holes with small accelerations are stable against linear scalar perturbations.

First law for Kerr Taub-NUT AdS black holes

The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this work, we investigate the thermodynamics of Kerr Taub-NUT AdS black holes. We present geometric Komar definitions for the black hole charges, that by construction satisfy the Smarr formula. Further, by a scaling argument based on Euler’s theorem, we establish the first law for the Kerr Taub-NUT AdS black holes. The corresponding first law includes variations in the cosmological constant, NUT charges and angular momenta. The key new ingredient in the construction are the independent variations of both angular momenta, the black hole and Misner string angular momenta. Employing the Brown-York quasi-local charge definitions we show that our expression for the mass and spin coincide with our generalized Komar expressions. We indicate the relevance of these results to the thermodynamics of rotating AdS black holes, including the proper choice of time-like Killing vector to produce the correct thermodynamic mass.

Energy extraction from AdS black holes via superradiance

Superradiance is known as a wave amplification process caused by rotating or charged black holes. We argue that the superradiance of stationary black holes in asymptotically AdS spacetimes can be characterized by the ability of energy extraction. Specifically, we demonstrate that energy can be extracted from Reissner-Nordström-AdS4 and Kerr-AdS4 under appropriate time-dependent boundary conditions at conformal boundaries. This indicates that energy can be extracted from thermal states dual to these black holes by applying appropriate time-dependent sources. We also show that the energy extraction can be realized as a reversible process.

RPS thermodynamics of Taub–NUT AdS black holes in the presence of central charge and the weak gravity conjecture

We study the thermodynamics of the Taub–NUT AdS black holes by Visser’s holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables P and V, we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub–NUT black holes e.g. supercritical phase equilibrium in the $$T-S$$ processes, $$Q-\Phi $$ and the Hawking-Page phase transition in the $$\mu -C$$ processes. As a consequence, the consistency of the weak gravity conjecture of multi-charge for Taub–NUT-AdS black holes at critical points is proved. We conclude that in the presence of the central charge and assuming $$C=\frac{3}{8}\ell ^2$$ , weak gravity conjecture could be satisfied in the Taub–NUT-AdS black holes with $${\hat{n}}\ll 1$$ .

Overview of thermodynamical properties for Reissner–Nordström–de Sitter spacetime in induced phase space

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner–Nordström (RN) black hole are not independent with each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN–dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the laws of thermodynamics still hold on. In our work, the thermodynamic properties of the RN–dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN–dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule–Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvatures of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN–dS spacetime, which opens a new window to investigate the dS spacetime with black holes from an observational perspective.

Effects of a global monopole on the thermodynamic phase transition of a charged AdS black hole* *Supported by the National Natural Science Foundation of China (11873001, 12047564), the Fundamental Research Funds for the Central Universities (2021CDJZYJH-003) and the Postdoctoral Science Foundation of Chongqing (cstc2021jcyj-bsh0124)

We study the dynamical properties of the thermodynamic phase transition (PT) of a charged AdS black hole (BH) with a global monopole via the Gibbs free energy landscape and reveal the effects of the global monopole on the kinetics of thermodynamic PTs. First, we briefly review the thermodynamics of a charged AdS BH with a global monopole. Then, we introduce the Gibbs free energy landscape to investigate the thermodynamic stability of the BH states. Because of thermal fluctuations, the small black hole (SBH) state can transit to a large black hole (LBH) state, and vice versa. Further, we use the Fokker-Planck equation with the reflecting boundary condition to study the probability evolution of the BH state with and without a global monopole separately. It is found that for both the SBH and LBH states, the global monopole could slow down the evolution of the BH state. In addition, we obtain the relationship between the first passage time and the monopole parameter η. The result shows that as the monopole parameter η increases, the mean first passage time becomes longer for both the SBH and LBH states.

Shadow thermodynamics of non-linear charged Anti-de Sitter black holes* *Supported by the National Natural Science Foundation of China (12075143)

It is well known that when vacuum polarization emerges in quantum electrodynamics, the non-linear interaction between electromagnetic fields should be considered. Moreover, the corresponding field of non-linear electrodynamics can have important effects on black hole physics. In this work, we focus on the relationship between an observable quantity, that is, the shadow radius, and the first-order phase transition of non-linear charged AdS black holes in the framework of Einstein-power-Yang-Mills gravity. The results show that, under a certain condition, there exists a first-order phase transition from the viewpoint of both the shadow radius and horizon radius, which depend on temperature (or pressure). From the viewpoint of the shadow radius, the phase transition temperature is higher than that from the viewpoint of the horizon radius under the same condition. This may be due to the non-linear Yang Mills charge and the gravitational effect. This indicates that the shadow radius can be regarded as a probe to reveal the thermodynamic phase transition information of black holes. The thermal profiles of coexistent large and small black hole phases when the system is undergoing the phase transition are presented for two different values of the non-linear Yang Mills charge parameter: . Furthermore, the effects of the non-linear Yang Mills charge parameter on the shadow radius and thermal profile are investigated.

Charged black holes from a family of Born–Infeld-type electrodynamics models

We present a family of nonlinear electrodynamics models that are free of the infinite self-energy of the point charge. Each model is dependent on a dimensional nonlinearity parameter and is determined by the integer value of a dimensionless parameter [Formula: see text]. The Born–Infeld model is recovered when [Formula: see text]. Some of the characteristics of this family are studied. In addition, we study the solutions of electrically charged AdS black holes, which result from coupling these electrodynamic models to General Relativity. A Smarr formula consistent with the first law of thermodynamics is also obtained in an extended phase space.

A comment on a fine-grained description of evaporating black holes with baby universes

We study a partially fine-grained description of an evaporating black hole by introducing an open baby universe with a boundary. Since the Page’s calculation of the entropy of Hawking radiation involves an ensemble average over a class of states, one can formally obtain a fine-grained state by purifying this setup. For AdS black holes with a holographic dual, this purification amounts to introducing an additional boundary (i.e., baby universe) and then connecting it to the original black hole through an Einstein-Rosen bridge. We uncover several details of this setup. As applications, we briefly discuss how this baby universe modifies the semi-classical gravitational Gauss law as well as the gravitational dressing of operators behind the horizon.

The timbre of Hawking gravitons: an effective description of energy transport from holography

Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index 3 − d for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.

Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions

In higher dimensions, we study Degenerate-Higher-Order-Scalar-Tensor theories and we derive solutions that resemble the Schwarzschild Anti-de Sitter black holes. We compute their thermodynamic quantities following the Wald formalism, satisfying the First Law of Thermodynamics and a higher dimensional Smarr relation. Constructing a Noether charge with a suitable choice of a space-like Killing vector, we obtain the shear viscosity of the non-gravitational dual field theory, where for a suitable choice of the couplings functions, the Kovtun-Son-Starinets bound is violated. These results are corroborated by the calculation of the Green's functions following the Kubo formalism.

Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner–Nordström AdS BH in standard Einstein gravity.

The phase diagram of BPS black holes in AdS5

Motivated by recent studies of supersymmetric black holes, we revisit the phase diagram of AdS black holes, whether BPS or not, with particular emphasis on the role of rotation. We develop BPS thermodynamics systematically and, in many explicit examples, we study its striking similarities with more familiar AdS black holes, as well as some differences. We highlight an important fugacity that preserves BPS saturation but is not captured by the supersymmetric index.

NED-AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion

We study and discuss the critical behaviour of charged by nonlinear electrodynamics (NED) AdS black holes in an extended phase space. The negative cosmological constant is treated as a thermodynamic pressure and the black hole mass is considered as the chemical enthalpy. We show the analogy of thermodynamics and phase transitions studied with the Van der Walls liquid–gas system. We introduce new thermodynamic quantities conjugated to the NED coupling and a magnetic charge. It was demonstrated that the first law of black hole thermodynamics and the Smarr relation hold. We have calculated the Joule–Thomson thermodynamic coefficient and inversion temperature, and the Joule–Thomson adiabatic expansion is investigated.

Hawking-Page phase transition of the Schwarzschild AdS black hole with the effective Tolman temperature

A sufficiently large Schwarzschild AdS black hole with the Hawking temperaturehas a positive heat capacity and undergoes the Hawking-Page phase transition.Even though an arbitrary isothermal surface of a cavityis introduced, the essential features about the stability and phase transition of theSchwarzschild AdS black hole remain the same.In this paper, we study the stability and the Hawking-Page phase transition of the Schwarzschild AdS black hole by employing an alternative local temperature satisfying the Hartle-Hawking vacuum condition which states thatthe ingoing and outgoing fluxes vanish at the horizon so that the local temperature is naturally zero there.The different definition of the local temperature based on the stress tensor approachprovides different types of stability and phase transition.For a AdS curvature radius below a critical one,the medium-sized black hole is found to be stable and the other small and large black holes turnout to be unstable regardless of the AdS curvature radius.Furthermore, we encounter various critical temperatures.The first one is for the Hawking-Page phase transition between the medium-sized black hole and thermal AdS, andthe second one is for a phase transition between the large black hole and thermal AdS; however, the latter one is not essential becausethe large black hole and thermal AdS eventually collapse to the medium-sized black hole.Interestingly, we find an additional critical temperature related to the zeroth-orderphase transition between the medium-sized black hole and thermal AdS.Consequently, the medium-sized black hole undergoes both the Hawking-Page phase transitionand the zeroth-order phase transition.

On the time dependence of holographic complexity for charged AdS black holes with scalar hair

In the presence of a scalar hair perturbation, the Cauchy horizon of a Reissner-Nordström black hole disappears and is replaced by the rapid collapse of the Einstein-Rosen bridge, which leads to a Kasner singularity [1, 2]. We study the time-dependence of holographic complexity, both for the volume and for the action proposals, in a class of models with hairy black holes. Volume complexity can only probe a portion of the black hole interior that remains far away from the Kasner singularity. We provide numerical evidence that the Lloyd bound is satisfied by the volume complexity rate in all the parameter space that we explored. Action complexity can instead probe a portion of the spacetime closer to the singularity. In particular, the complexity rate diverges at the critical time tc for which the Wheeler-DeWitt patch touches the singularity. After the critical time the action complexity rate approaches a constant. We find that the Kasner exponent does not directly affect the details of the divergence of the complexity rate at t = tc and the late-time behaviour of the complexity. The Lloyd bound is violated by action complexity at finite time, because the complexity rate diverges at t = tc. We find that the Lloyd bound is satisfied by the asymptotic action complexity rate in all the parameter space that we investigated.

Thermodynamics and phase transition of d-dimensional charged AdS black hole in rainbow gravity

In this paper, we have studied the thermodynamic properties of charged AdS black hole with different dimensions under rainbow gravity. At first, by employing the Heisenberg uncertainty principle and the modified dispersion relation and analyzing the effect of rainbow gravity parameter [Formula: see text] and AdS radius [Formula: see text] on the thermodynamics and phase transformation, we have found that the phase structure is related to the AdS radius [Formula: see text] and the heat capacity behaviors are quite similar for different rainbow gravity parameters [Formula: see text] and different dimensions [Formula: see text]. Then, for the rainbow gravity, introducing the analogy between the charged AdS black hole and liquid–gas systems and analyzing the critical behavior of the state equation for charged AdS black hole in different dimensions, the charged AdS black hole has Van der Waals-like phase transitions. At last, we have discussed the relationship between Gibbs free energy [Formula: see text] and Hawking temperature [Formula: see text] in different dimensions and found the typical dovetail behavior, which can be interpreted as a first-order phase transition for the charged AdS black hole under rainbow gravity.

Holographic CFT phase transitions and criticality for charged AdS black holes

We study the holographic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton’s constant. In the dual CFT this corresponds to including the central charge C and its chemical potential μ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy (T, S), electric potential vs. charge ( overset{sim }{Phi},overset{sim }{Q} ) and field theory pressure vs. volume (p, mathcal{V} ). For the (grand) canonical ensembles at fixed ( overset{sim }{Q},mathcal{V},C ), ( overset{sim }{Phi},mathcal{V},C ) and ( overset{sim }{Q},mathcal{V},mu ), based on the holographic dictionary, we argue the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed ( overset{sim }{Q},mathcal{V},mu ) we find a new zeroth-order phase transition between a high- and low-entropy phase at some μ-dependent temperature. Finally, we point out there is no critical behaviour in the fixed p ensembles, i.e. there is no p − mathcal{V} criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid. Whether or not this phase structure is supported by CFT computations remains an interesting open question.

Complexity via replica trick

We consider the complexity of a single-sided AdS black hole as modelled by an end-of-the-world brane. In addition we present multi-boundary partition functions and matter correlation functions for such a setting. We compute the complexity using a modified replica trick corresponding to the “quenched geodesic length” in JT gravity. The late time behaviour of complexity shows a saturation to a constant value of order eS0 following a period of linear growth. Furthermore, we show that our approach leads to an improved result for the variance of complexity, namely it being time-independent at late times. We conclude by commenting on the introduction of dynamical end-of-the-world branes.

Tsallis entropy inspires geometric thermodynamics of specific black hole

In this paper, we analyze the thermodynamics of five-dimensional Schwarzschild AdS black hole in AdS_5 times S^5 spacetime in the presence of Tsallis entropy. Since the cosmological constant Lambda is considered as thermodynamical pressure with volume as its conjugate, but this explanation cannot be employed in AdS/CFT correspondence. In this study, we associate cosmological constant Lambda in boundary gauge theory with the number of colors N and chemical potential is taken to be its thermodynamic conjugate. The two geometric parameters in the AdS black hole, r and L are substituted for two thermodynamic parameters in the micro-canonical ensemble, which are considered to be entropy S and N^2. Moreover, we evaluate several thermodynamical geometry formulations, including Weinhold, Ruppeiner, and Quevedo and derive associated scalar curvatures for five-dimensional Schwarzschild AdS black hole. It is suggested that all these geometries show repulsive/attractive forces on the particles at different phases of entropy.