Thermodynamics and Stability of Higher Dimensional Rotating (Kerr) AdS Black Holes

TL;DR

This paper investigates the thermodynamic and gravitational stability of higher-dimensional Kerr-AdS black holes, revealing conditions under which they are stable and thermodynamically favored, with notable differences in five and six or more dimensions.

Contribution

It provides a detailed analysis of stability conditions for Kerr-AdS black holes in higher dimensions, highlighting the effects of rotation parameters and dimensionality.

Findings

Kerr-AdS black holes become stable when rotation parameters are comparable to the AdS radius.

Thermal equilibrium with radiation requires rotation parameters not significantly smaller than the AdS radius.

In five dimensions, no high-temperature thermal AdS phase exists regardless of rotation parameters.

Abstract

We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six dimensional case is marginal.