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

TL;DR

This paper introduces a superpotential-based method to compute quasi-normal modes of AdS black holes, providing a new approach inspired by the exact solutions for BTZ black holes and applying it to five-dimensional cases.

Contribution

A novel superpotential approach for calculating quasi-normal modes of AdS black holes, extending the method to higher dimensions and revealing proportionality to surface gravity.

Findings

Quasi-normal modes are proportional to surface gravity for small and large black holes.

The method successfully computes modes for five-dimensional Schwarzschild AdS black holes.

Small black holes exhibit known instabilities in AdS space.

Abstract

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-deSitter 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-deSitter space.