Exact Gravitational Quasinormal Frequencies of Topological Black Holes

TL;DR

This paper derives exact gravitational quasinormal frequencies for massless topological black holes in anti-de Sitter space using gauge-invariant formalism and hypergeometric functions, providing precise analytic results.

Contribution

It presents the first exact analytic calculation of gravitational quasinormal modes for these black holes, simplifying the problem to solvable scalar equations.

Findings

Exact quasinormal frequencies obtained for all modes

Reduction to hypergeometric equations enables precise solutions

Applicable to d-dimensional anti-de Sitter topological black holes

Abstract

We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.