Charged and rotating AdS black holes and their CFT duals

TL;DR

This paper explores charged and rotating AdS black holes, their stability, and dual CFT descriptions, revealing differences between weak and strong coupling regimes, including phase transitions and divergences.

Contribution

It analyzes the stability of rotating and charged AdS black holes and compares their CFT duals at weak and strong coupling, highlighting new limits and divergence behaviors.

Findings

Black holes with negative action are thermodynamically stable and prevent superradiance.

Bose-Einstein condensation occurs at weak coupling but not at strong coupling.

Finite temperature effects modify the usual 4/3 factor in the free CFT and supergravity comparison.

Abstract

Black hole solutions that are asymptotic to $ AdS_5 \times S^5$ or $ AdS_4 \times S^7$ can rotate in two different ways. If the internal sphere rotates then one can obtain a Reissner-Nordstrom-AdS black hole. If the asymptotically AdS space rotates then one can obtain a Kerr-AdS hole. One might expect superradiant scattering to be possible in either of these cases. Superradiant modes reflected off the potential barrier outside the hole would be re-amplified at the horizon, and a classical instability would result. We point out that the existence of a Killing vector field timelike everywhere outside the horizon prevents this from occurring for black holes with negative action. Such black holes are also thermodynamically stable in the grand canonical ensemble. The CFT duals of these black holes correspond to a theory in an Einstein universe with a chemical potential and a theory in a rotating Einstein universe. We study these CFTs in the zero coupling limit. In the first case, Bose-Einstein condensation occurs on the boundary at a critical value of the chemical potential. However the supergravity calculation demonstrates that this is not to be expected at strong coupling. In the second case, we investigate the limit in which the angular velocity of the Einstein universe approaches the speed of light at finite temperature. This is a new limit in which to compare the CFT at strong and weak coupling. We find that the free CFT partition function and supergravity action have the same type of divergence but the usual factor of 4/3 is modified at finite temperature.