Black hole dynamics from thermodynamics in Anti-de Sitter space

We examine the thermodynamic stability of large black holes in four-dimensional anti-de Sitter space, and we demonstrate numerically that black holes which lack local thermodynamic stability often also lack stability against small perturbations. This shows that no-hair theorems do not apply in anti-de Sitter space. A heuristic argument, based on thermodynamics only, suggests that if there are any violations of Cosmic Censorship in the evolution of unstable black holes in anti...

We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase tra...

The thermodynamic properties of Schwarzschild-anti-de Sitter black holes confined within finite isothermal cavities are examined. In contrast to the Schwarzschild case, the infinite cavity limit may be taken which, if suitably stated, remains double valued. This allows the correspondence between non-existence of negative modes for classical solutions and local thermodynamic stability of the equilibrium configuration of such solutions to be shown in a well defined manner. This...

We investigate the thermodynamical properties of black holes in (3+1) and (2+1) dimensional Einstein gravity with a negative cosmological constant. In each case, the thermodynamic internal energy is computed for a finite spatial region that contains the black hole. The temperature at the boundary of this region is defined by differentiating the energy with respect to entropy, and is equal to the product of the surface gravity (divided by~$2\pi$) and the Tolman redshift factor...

We investigate the Schwarzschild-Anti-deSitter (SAdS) and SdS BH thermodynamics in 5d higher derivative gravity. The interesting feature of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. The appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur or...

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, which change 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 temperature of the black hole canno...

In these lecture notes we discuss recently conjectured instability of anti-de Sitter space, resulting in gravitational collapse of a large class of arbitrarily small initial perturbations. We uncover the technical details used in the numerical study of spherically symmetric Einstein-massless scalar field system with negative cosmological constant that led to the conjectured instability.

We compute the mass and the temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient $\alpha_2<0$ in anti-de Sitter space and perform the stability analysis of topological black holes. When $k=-1$, the third order Lovelock black holes are thermodynamically stable for the whole range $r_+$. When $k=1$, we found that the black hole has an intermediate unstable phase for $D=7$. In eight dimensional spacetimes, however, a new phase of thermodynamical...

We study the properties of anti--de Sitter black holes with a Gauss-Bonnet term for various horizon topologies (k=0, \pm 1) and for various dimensions, with emphasis on the less well understood k=-1 solution. We find that the zero temperature (and zero energy density) extremal states are the local minima of the energy for AdS black holes with hyperbolic event horizons. The hyperbolic AdS black hole may be stable thermodynamically if the background is defined by an extremal so...

We construct a covariant phase space for Einstein gravity in dimensions d>=4 with negative cosmological constant, describing black holes in local equilibrium. Thus, space-times under consideration are asymptotically anti-de Sitter and admit an inner boundary representing an isolated horizon. This allows us to derive a first law of black hole mechanics that involves only quantities defined quasi-locally at the horizon, without having to assume that the bulk space-time is stati...