Rotation and the AdS/CFT correspondence

TL;DR

This paper explores the thermodynamics of rotating black holes in anti-de Sitter space and their dual conformal field theories, including a new five-dimensional solution, highlighting divergences at critical angular velocities.

Contribution

It introduces a new five-dimensional Kerr-AdS black hole solution and analyzes the thermodynamic behavior of dual CFTs at critical rotation limits.

Findings

Divergences in partition functions and black hole actions at critical angular velocities.

Existence of thermodynamic equilibrium for rotating black holes in AdS space.

New five-dimensional Kerr-AdS black hole solution.

Abstract

In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be co-rotating faster than light far from the black hole. However in asymptotically anti-de Sitter space such equilibrium is possible for certain ranges of the parameters. We examine the relationship between conformal field theory in rotating Einstein universes of dimensions two to four and Kerr anti-de Sitter black holes in dimensions three to five. The five dimensional solution is new. We find similar divergences in the partition function of the conformal field theory and the action of the black hole at the critical angular velocity at which the Einstein rotates at the speed of light. This should be an interesting limit in which to study large $N$ Yang-Mills.