Perturbative calculation of quasi-normal modes of Schwarzschild black holes

TL;DR

This paper presents an analytical method to calculate the asymptotic quasi-normal mode frequencies of Schwarzschild black holes, providing explicit first-order corrections for different spins, aligning with previous numerical and WKB results.

Contribution

It introduces a systematic perturbative approach to derive explicit first-order corrections to quasi-normal mode frequencies for Schwarzschild black holes.

Findings

First-order correction expressions derived for various spins.

Results agree with existing WKB and numerical analyses.

Method enhances analytical understanding of black hole perturbations.

Abstract

We discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of a four-dimensional Schwarzschild black hole by expanding around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. We obtain an explicit expression for the first-order correction and arbitrary spin. Our results are in agreement with the results from WKB and numerical analyses in the case of gravitational waves.