Perturbative calculation of quasi-normal modes

TL;DR

This paper presents a systematic analytical method for calculating the asymptotic quasi-normal mode frequencies of black holes, extending previous approaches and confirming results with numerical analysis.

Contribution

It introduces a perturbative approach to compute quasi-normal modes for Schwarzschild and AdS black holes, improving analytical understanding.

Findings

Analytical results agree with numerical data

Extended the method to five-dimensional AdS black holes

Provided a systematic perturbative framework

Abstract

I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole, I discuss a perturbative solution of the Heun equation. The analytical results are in agreement with the results from numerical analysis.