Semiclassical instabilities of Kerr-AdS black holes

TL;DR

This paper investigates the thermodynamic stability of Kerr-AdS black holes by analyzing perturbative corrections to the gravitational partition function, identifying critical stability conditions through numerical solutions of coupled PDEs.

Contribution

It provides a numerical analysis of the eigenvalue problem for metric perturbations, linking gravitational instabilities to thermodynamic stability in rotating black holes.

Findings

Negative mode indicates the line of critical stability.

Numerical solutions agree with thermodynamic stability criteria.

Highlights importance of gravitational partition functions beyond instanton approximation.

Abstract

We study the thermodynamic stability of the Kerr-AdS black hole from the perturbative corrections to the gravitational partition function. The line of critical stability is identified by the appearance of a negative mode of the Euclidean action that renders the partition function ill-defined. The eigenvalue problem, consisting of a system of three coupled partial differential equations for the metric perturbations, is solved numerically. The agreement with the standard condition of thermodynamic stability in the grand canonical ensemble is remarkable. The results illustrate the physical significance of gravitational partition functions for rotating spacetimes beyond the instanton approximation.