Bjorken flow from an anti-de Sitter space Schwarzschild black hole

We consider a large black hole in asymptotically anti-de Sitter spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions.     

Thermodynamics of black holes in anti-de Sitter space

The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.     

Entropy spectrum of a Kerr anti-de Sitter black hole

The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr–Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equally spaced.     

(2+1)-dimensional charged black hole in topologically massive electrodynamics

The 2+1 black hole coupled to a Maxwell field can be charged in two different ways. Besides a Coulomb field, whose potential grows logarithmically in the radial coordinate, there also exists a topological charge due to the existence of a noncontractible cycle. The topological charge does not gravitate and is somehow decoupled from the black hole. This situation changes if one turns on the Chern-Simons term for the Maxwell field. First, the flux integral at infinity becomes equal to the topological charge. Second, demanding regularity of the black hole horizon, the Coulomb charge must vanish identically. Hence, in 2+1 topologically massive electrodynamics coupled to gravity, the black hole can support holonomies only for the Maxwell field. This means that the charged black hole is constructed from the vacuum by means of spacetime identifications.     

Regular black hole remnants in de Sitter space

We address the question of thermodynamical evolution of regular spherically symmetric cosmological black holes with de Sitter center. Space–time is asymptotically de Sitter as r→0$r\to 0$ and as r→∞$r\to \infty$. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress–energy tensor. In the range of masses M_cr1?M?M_cr2$M_{cr1}?M?M_{cr2}$ it describes a regular cosmological black hole with three horizons, an internal horizon ra$r_a$, a black hole horizon rb>ra$r_b>r_a$, and a cosmological horizon rc>rb$r_c>r_b$. Thermodynamical preference for a final product of evaporation is a double-horizon (ra=rb$r_a=r_b$) black hole remnant with the positive specific heat.     

Abundant stable gauge field hair for black holes in anti-de Sitter space

We present new hairy black hole solutions of SU(N) Einstein-Yang-Mills (EYM) theory in asymptotically anti-de Sitter (AdS) space. These black holes are described by N+1 independent parameters and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for a sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in AdS can be endowed.     

Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.     

Fermion tunnels of higher-dimensional anti-de Sitter Schwarzschild black hole and its corrected entropy

Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the “tortoise” coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r−t) sector is important to our research. Because we only need to study the (r−t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.     

Thermodynamic and geometric framework of a （2＋ 1）-dimensional black hole with non-linear electrodynamics

The thermodynamic properties of a (2 + 1)-dimensional black hole with non-linear electrodynamics from the viewpoint of geometry is studied and some kinds of temperatures of the black hole have been obtained. Weinhold curvature and Ruppeiner curvature are explored as information geometry. Moreover, based on Quevedo's theory, the Legendre invariant geometry is investigated for the black hole. We also study the relationship between the scalar curvatures of the above several metrics and the phase transitions produced from the heat capacity.     

Critical behaviors of a (2 + 1)-dimensional black hole with a nonlinear electrodynamics source

On the basis of a charged BTZ black hole, we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics. In this way we artificially construct a (2 + 1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source. The thermodynamic quantities and Smarr formula are derived. It is found that this black hole has T−S criticality like that of an RN-AdS black hole. Further modifying the metric function, we obtain a (2 + 1)-dimensional black hole possessing P−V critical behaviors similar to that of van der Waals fluid. To our knowledge, this is the first example of (2 + 1)-dimensional black holes having this kind of critical behavior.