  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory