Perturbative calculation of quasi-normal modes of AdS Schwarzschild black holes

TL;DR

This paper analytically computes first-order corrected quasi-normal modes of AdS Schwarzschild black holes for various perturbations, providing the first such analytic results for electromagnetic cases and confirming numerical findings.

Contribution

It introduces the first analytical calculation of electromagnetic quasi-normal modes with first-order corrections, extending previous numerical approaches.

Findings

Analytic expressions match numerical results.

First-order correction is logarithmic.

Electromagnetic modes are analytically derived for the first time.

Abstract

We calculate analytically quasi-normal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasi-normal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic.