Abstract

It is of considerable interest to know about the stability of black hole (and black brane) solutions in general relativity including in the presence of various matter fields, or in higher dimensions. Unfortunately, already the linear stability analysis of even the simplest backgrounds, such as the 4-dimensional Schwarzschild solution, let alone the Kerr metric, is not a trivial task. In these cases, one has available the classic Regge-Wheeler-Zerilli resp. Teukolsky formalism. However, in the case of higher dimensional stationary black holes, a formalism of similar power is not known to date. In this talk I present a variational approach to this problem put forward in a recent paper with Bob Wald. The approach also gives a conceptual understanding of why the approach based on the ``local Penrose inequality’’, put forward recently by Figueras et al., works, and it also allows one to demonstrate the ``Gubser Mitra conjecture’’ relating dynamical stability/instability of black holes to a natural notion of ``thermodynamical stability/instability’’.