Quasi-normal modes of AdS black holes: a superpotential approach

A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five-dimensional Schwarzschild anti-de Sitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well known instability of small black holes in anti-de Sitter space.