Asymptotic form of quasi-normal modes of large AdS black holes

TL;DR

This paper analytically derives the asymptotic quasi-normal mode frequencies of large five-dimensional AdS black holes by approximating the wave equation with hypergeometric functions, confirming numerical results and comparing with the 3D case.

Contribution

It introduces an analytical method to determine asymptotic quasi-normal frequencies for large AdS black holes, simplifying the Heun equation to a hypergeometric form.

Findings

Asymptotic frequencies match numerical results

Heun equation approximated by hypergeometric equation at large frequencies

Comparison with exact 3D case confirms validity

Abstract

We discuss a method of calculating analytically the asymptotic form of quasi-normal frequencies for large AdS black holes in five dimensions. In this case, the wave equation reduces to a Heun equation. We show that the Heun equation may be approximated by a Hypergeometric equation at large frequencies. Thus we obtain the asymptotic form of quasi-normal frequencies in agreement with numerical results. We also present a simple monodromy argument that leads to the same results. We include a comparison with the three-dimensional case in which exact expressions are derived.