Thermodynamics and weak cosmic censorship conjecture of an AdS black hole with a monopole in the extended phase space

The first law of black hole thermodynamics has been shown to be valid in the extended phase space.However,the second law and the weak cosmic censorship conjecture have not been investigated extensively.We investigate the laws of thermodynamics and the weak cosmic censorship conjecture of an AdS black hole with a global monopole in the extended phase space in the case of charged particle absorption.It is shown that the first law of thermodynamics is valid,while the second law is violated for the extremal and near-extremal black holes.Moreover,we find that the weak cosmic censorship conjecture is valid only for the extremal black hole,and that it can be violated for the near-extremal black holes,which is different from the previous results.     

Vacum Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein‘s GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.     

Vacuum Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein‘s GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.     

Quantization of Horizon Area of Kerr–Newman–de Sitter Black Hole

Using the adiabatic invariant action and applying the Bohr–Sommerfeld quantization rule and first law of black hole thermodynamics, a study of the quantization of the entropy and horizon area of a Kerr–Newman–de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters. Also, the corresponding quantum of horizon area is in agreement with the results of Bekenstein.     

Effects of thermal fluctuations on the Kerr–Newman–NUT–AdS black hole

This paper is devoted to studying the impact of thermal fluctuations on thermodynamics of rotating as well as charged anti-de Sitter black holes with the Newman–Unti–Tamburino(NUT)parameter. To this end, we derive the analytic expression of thermodynamic variables, namely the Hawking temperature, volume, angular velocity, and entropy within the limits of extended phase space. These variables meet the first law of thermodynamics as well as the Smarr relation in the presence of new NUT charge. To analyze the effects of quantum fluctuations, we derive the exact expression of corrected entropy, which yields modification in other thermodynamical equations of state. The local stability and phase transition of the considered black hole are also examined through specific heat. It is found that the NUT parameter increases the stability of small black holes, while the logarithmic corrections induce instability in the system.     

Thermodynamics of warped anti-de Sitter black holes under scattering of scalar field

We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field.Under scattering,conserved quantities can be transferred from the scalar field to the black hole,thereby changing the state of the black hole.We determine that the changes in the black hole are well coincident with the laws of thermodynamics.In particular,the Hawking temperat-ure of the black hole cannot be zero in the process as per the third law of thermodynamics.Furthermore,the black hole cannot be overspun bevond the extremal condition under the scattering of any mode of the scalar field.     

Strong cosmic censorshiP for a scalar field in a logarithmic-de Sitter black hole

It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship(SCC).Relevant issues for Reissner-Nordstrom-de Sitter(RN-dS)black holes and Born-Infeld-de Sitter black holes have been discussed.In this paper,we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields.It has been argued that SCC can be violated in a near-extremal RN-dS black hole.However,we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de Sitter black hole.Compared with Born-Infeld model,we find that the NLED effect has similar behavior.     

Hawking radiation as tunnelling from arbitrarily dimensional Reissner-Nordstrom de Sitter black hole

This paper extends Parikh-Wilzcek＇s recent work, which treats the Hawking radiation as a semi-classical tunnelling process from the event horizon of four dimensional Schwarzshild and Reissner-Nordstrom black holes, to that of arbitrarily dimensional Reissner-Nordstrom de Sitter black hole. The result shows that the tunnelling rate is related to the change of Bekenstein-Hawking entropy and the factually radiant spectrum is no longer precisely thermal after taking the dynamical black hole background and energy conservation into account, but is consistent with the underlying unitary theory and then satisfies the first law of the black hole thermodynamics. Meanwhile, in Parikh-Wilzcek＇s framework, this paper points out that the information conservation is only suitable for the reversible process but in highly unstable evaporating black hole （irreversible process） the information loss is possible.     

Entropy in the NUT—Kerr—Newman Black Holes in the Background of de Sitter Spacetime

We calculate the entropy of the fermion field in the NUT-Kerr-Newman black holes in the background of the de Sitter spacetime by using the improved brick-wall method and the membrane model.Here the Euler characteristic of the black holes is over two.The results show that,as the cut-off is properly chosen,the entropy in the black hole satisfies the Bekenstein-Hawking area law.     

Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties,but the black hole solutions in this theory are still not fully understood.In the paper,we concentrate on studying the charged black holes in such a theory.Adding the electromagnetic field part to the effective action,we show how the black hole solutions around the Reissner-Nordstrom metric can be solved perturbatively and iteratively.We further calculate the corresponding temperature,entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.     

Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity

We study the quasinormal modes(QNMs) of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional(5D) Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.     

Thermodynamic properties of Reissner-Nordstrm-de Sitter quintessence black holes

The mass,electric charge,and temperature of black holes in the Reissner-Nordstrm-de Sitter quintessence(RN-dSQ) spacetime are obtained.The heat capacities of the RN-dSQ black holes for certain electric charges and masses are analyzed.The electrostatic energy and dark energy in the RN-dSQ black holes are also calculated.     

Regular Black Holes with Cosmological Constant

We present a class of regular black holes with cosmological constant Λ in nonlinear electrodynamics. Instead of usual singularity behind black hole horizon, all fields and curvature invariants are regular everywhere for the regular black holes. Through gauge invariant approach, the linearly dynamical stability of the regular black hole is studied. In odd-parity sector, we find that the Λ term does not appear in the master equations of perturbations, which shows that the regular black hole is stable under odd-parity perturbations. On the other hand, for the even-parity sector, the master equations are more complicated than the case without the cosmological constant. We obtain the sufficient conditions for stability of the regular black hole. We also investigate the thermodynamic properties of the regular black hole, and find that those thermodynamic quantities do not satisfy the differential form of first law of black hole thermodynamics. The reason for violating the first law is revealed.     

Degenerate black rings in D=5 minimal supergravity

We consider both gauged and ungauged minimal supergravities in five dimensions and analyse the charged rotating solutions with two equal angular momenta J. When the electric charge Q～J~(2/3) with some specific coefficient, we find new extremal black objects emerge that are asymptotic to either Minkowski or global Ad S spacetimes and can be best described as degenerate black rings. Their near-horizon geometry is locally AdS_3×S~2, where the periodic U(1) fibre coordinate in S_3 untwists and collapses to be the degenerate part of the AdS_3 horizon. It turns out that there are two branches of extremal rotating black holes, starting as the extremal RN black holes of the same mass, but opposite charges. With the increasing of the angular momentum, they will join to become the same degenerate black ring, where the Gibbs free energies however are not continuous at the joining. For the same Q(J) relation, we find that there is in addition a rotating soliton whose mass is smaller than that of the degenerate black ring.     

Microscopic states of Kerr black holes from boundary-bulk correspondence

It was previously claimed by the author that black holes can be considered as topological insulators. Both black holes and topological insulators have boundary modes, and the boundary modes can be described by an effective BF theory. In this paper, the boundary modes on the horizons of black holes are analyzed using methods developed for topological insulators. BTZ black holes are analyzed first, and the results are found to be compatible with previous works. The results are then generalized to Kerr black holes, for which new results are obtained: dimensionless right-and left-temperatures can be defined and have well behavior in both the Schwarzschild limit a → 0 and the extremal limit a → M. Upon the Kerr/CFT correspondence, a central charge c = 12 Mr+ can be associated with an arbitrary Kerr black hole. Moreover, the microstates of the Kerr black hole can be identified with the quantum states of this scalar field. From this identification, the number of microstates of the Kerr black hole can be counted, yielding the Bekenstein-Hawking area law for the entropy.     

Extended Phase Space in the Framework of Holography

We consider a holographic extended phase space in the presence of Reissner-Nordstrom-Anti-de Sitter(RNAdS) and Born-Infeld-Anti-de Sitter(BI-AdS) black holes in the bulk. In this extended phase space the cosmological constant is investigated as pressure and volume is defined as the codimension one-time slice in the bulk geometry enclosed by the minimal area appearing in the computation of the holographic entanglement entropy. These thermodynamics quantities can serve as probes of the underlying phase transition dictated by black hole thermodynamics, but do not describe different structures. We find that the isocharges on the pressure-volume plane exhibit a Van der Waals-like structure, for RN-AdS black holes in the background. For BI-AdS black holes, we observe the analogy with a Van der Waals liquid-gas system for βQ 1/2 and Reentrant phase transition for βQ 1/2 in the holographic extended phase space. The same holographic thermodynamic behavior is observed when we use the fidelity susceptibility as the volume and the cosmological constant as the pressure for RN-AdS black hole in the background.     

Energy and first law of thermodynamics for Born-Infeld-anti-de-Sitter black hole

We calculate the local energy and the energy density of the Reisner-Norstrm-anti-de-Sitter black hole, study the first law of thermodynamics and show the Smarr formula for the Born-Infeld-anti-de-Sitter black hole. Applying the first law of thermodynamics to the black hole region, we analyse the three energy exchange processes between the black hole region and the outer and the inner regions.     

Entropy of Reissner—Nordstrom—De Sitter Black Hole in Nonthermal Equilibrium

By making use of the method of quantum statistics,we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black Hole and obtain the integral expression of black hole‘s entropy and the entropy to which the cosmic horizon surface corresponds.It avoids the difficulty in solving the wave equation of various particles.Then via the improved brick-wall method,i.e.the membrane model,we calculate black hole‘s entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon,the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon.In our result,the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.In the whole process,the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.     

Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes

In this paper, we describe quasinormal modes(QNMs) for gravitational perturbations of Einstein-GaussBonnet black holes(BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime(flat, de Sitter(d S) and anti-de Sitter(Ad S)). Our attention is concentrated on discussing the(in)stability of Einstein-Gauss-Bonnet Ad S BHs through the temporal evolution of all types of gravitational perturbation fields(tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore,the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet Ad S BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet Ad S BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds.     

A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism

In this note, the off-shell generalized Abbott–Deser–Tekin(ADT) formalism is applied to explore the mass of Kerr–anti-de Sitter(Kerr–AdS) black holes in various dimensions within asymptotically rotating frames. The cases in four and five dimensions are explicitly investigated. It is demonstrated that the asymptotically rotating effect may make the charge non-integrable or unphysical when the asymptotic non-rotating timelike Killing vector associated with the charge is allowed to vary and the fluctuation of the metric is determined by the variation of all the mass and rotation parameters.To obtain a physically meaningful mass, it is proposed that one can let the non-rotating timelike Killing vector be fixed or perform calculations in the asymptotically static frame. The results further support that the ADT formalism is backgrounddependent.