Topological Aspects of Entropy and Phase Transition of Kerr Black Holes

In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem,it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime.By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.     

P-V Criticality of Born-Infeld AdS Black Holes Surrounded by Quintessence

We discuss the P-V criticality and phase transition in the extended phase space of Born-Infeld AdS(BIAdS) black hole surrounded by quintessence dark energy, where the cosmological constant Λ is identified with the thermodynamical pressure P. Comparing with Van der Waals(VdW)-like SBH/LBH phase transition of Born-Infeld AdS(BI-AdS) black hole, we find that the BI-AdS black hole surrounded by quintessence dark energy possesses lower critical temperature because of parameter a 0, even disappears since the parameter a taking enough large values leads to Tc ≤ 0. Moreover, the interesting thermodynamic phenomenon of reentrant phase transition(RPT) are also observed,and the quintessence dark energy plays a similar role in this RPT.     

Information Loss for QCD Matter in AdS Black Holes at LHC

In this paper,we find the information loss for QCD matter in AdS black holes at LHC by extending the Gottesman and Preskill methode to AdS black holes.We calculate the information transformation from the collapsing matter to the state of outgoing Hawking radiation for both quarks and gluons.It is noticed that for finite values of quark and gluon energies,information from all emission processes experiences some degrees of loss.Possible explanation for this feature will be presented in this paper.     

On Phase Transitions near Black Holes

JETP Letters - It has been shown that temperatures near the horizon of rotating black holes can be about the phase transition temperature in the Standard Model with the Higgs boson. The distance...     

New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes

A new infinite series of Einstein metrics is constructed explicitly on S²×S³, and the non-trivial S³-bundle over S², containing infinite numbers of inhomogeneous ones. They appear as a certain limit of 5-dimensional AdS Kerr black holes. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Einstein metric on the non-trivial S^d–2-bundle over S² from a d-dimensional AdS Kerr black hole. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on      

Signature of Different Phases of Ricci Flat Black Holes and AdS Solitons in Gauss-Bonnet Gravity

From the perturbation around the background spacetimes in the Gauss Bonnet gravity, we find the physical evidence that Ricci fiat AdS black holes and AdS solitons are different physical configurations and stay in different phases, this serves as a strong support to the previous mathematical and thermodynamieal arguments.     

Black Hole Phase Transition in Massive Gravity

In massive gravity, some new phenomena of black hole phase transition are found. There are more than one critical points under appropriate parameter values and the Gibbs free energy near critical points also has some new properties. Moreover, the Maxwell equal area rule is also investigated and the coexistence curve of the black hole is given.     

Cosmological Black Holes

In this paper we propose a model for the formation of the cosmological voids. We show that cosmological voids can form directly after the collapse of extremely large wavelength perturbations into low-density black holes or cosmological black holes (CBH). Consequently the voids are formed by the comoving expansion of the matter that surrounds the collapsed perturbation. It follows that the universe evolves, in first approximation, according to the Einstein-Straus cosmological model. We discuss finally the possibility to detect the presence of these black holes through their weak and strong lensing effects and their influence on the cosmic background radiation.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Black Holes as Atoms

Stationary spacetimes containing a black hole have several properties akin to those of atoms. For instance, such spacetimes have only three classical degrees of freedom, or observables, which may be taken to be the mass, the angular momentum, and the electric charge of the hole. There are several arguments supporting a proposal originally made by Bekenstein that quantization of these classical degrees of freedom gives an equal spacing for the horizon area spectrum of black holes. We review some of these arguments and introduce a specific Hamiltonian quantum theory of black holes. Our Hamiltonian quantum theory gives, among other things, a discrete spectrum for the classical observables, and it produces an area spectrum which is closely related to Bekenstein's proposal. We also present a foamlike model of horizons of spacetime. In our model spacetime horizon consists of microscopic Schwarzschild black holes. Applying our Hamiltonian approach to this model we find that the entropy of any horizon is one quarter of its area.     

On Naked Black Holes

The recently proposed criteria for naked blackholes are conveniently rephrased. It is shown that twosolutions of dilaton-Maxwell gravity, satisfying weakenergy conditions, represent naked blackholes.     

Black Holes Are One-Dimensional

The holographic principle has revealed that phyical systems in 3-D space, black holes included, are basically two-dimensional as far as their information content is concerned. This conclusion is complemented by one sketched here: as far as entropy or information flow is concerned, a black hole behaves as a one-dimensional channel. We define a channel in flat spacetime in thermodynamic terms, and contrast it with common entropy emitting systems. A black hole is more like the former: its entropy output is related to the emitted power as it would be for a one-dimensional channel, and disposal of an information stream down a black hole is limited by the power invested in the same way as for a one-dimensional channel.     

Black holes,AdS, and CFTs

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein–Hawking entropy S _BH is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly while there is a valid context in which this result can be restated as “S _BH counts all states inside the black hole,” there may also be another in which it may be restated as “S _BH does not count all states inside the black hole, but only those that are distinguishable from the outside.” The arguments and conclusions represent the author’s translation of the community’s collective wisdom, combined with a few recent results.     

Noncommutative Singular Black Holes

In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact （t - r） dependence of solution in terms of the noncommutative parameter σ. In this setup, there Js no black hole remnant at long times.     

The Thermodynamic Geometry and Phase Transition of the Plane Symmetric Black Hole

In this paper, we investigate the thermodynamic properties and the thermodynamic geometry of the plane symmetric black hole. We obtain the thermodynamic curvature based on the Weinhold geometry curvature, Ruppeiner geometry curvature and the Quevedo curvature. We find the Weinhold curvature always equals to zero and there is a phase transition point for the Ruppeiner curvature. The Quevedo curvature produces a same phase structure as the heat capacity.

     

Spectroscopies of Extreme Black Holes

The spectroscopies of extreme black holes are investigated by the intrinsic property of these black holes in this paper. We find that the area spectrum of the extreme Reissner-Nordstrom black hole is dependent on the fine structure constant. While the area spectra share the same expression and are determined by the quantum numbers of angular momentum for the extreme Kerr-Sen Dilaton-Axion and Kaluza-Klein black holes.