The asymptotic quasinormal mode spectrum of non-rotating black holes

TL;DR

This paper derives the asymptotic quasinormal mode spectrum for non-rotating black holes using the WKB approximation, confirming previous results and revealing differences between Schwarzschild and Reissner-Nordstrom black holes.

Contribution

It provides simple derivations of asymptotic QNM conditions for Schwarzschild and Reissner-Nordstrom black holes, filling gaps in prior analyses and exploring the effects of charge.

Findings

Reaffirmation of previous asymptotic QNM results for Schwarzschild black holes.

Reissner-Nordstrom QNMs are generally not periodic in the imaginary frequency.

Charged black holes exhibit unique properties affecting their QNM interpretation.

Abstract

A conjectured connection to quantum gravity has led to a renewed interest in highly damped black hole quasinormal modes (QNMs). In this paper we present simple derivations (based on the WKB approximation) of conditions that determine the asymptotic QNMs for both Schwarzschild and Reissner-Nordstrom black holes. This confirms recent results obtained by Motl and Neitzke, but our analysis fills several gaps left by their discussion. We study the Reissner-Nordstrom results in some detail, and show that, in contrast to the asymptotic QNMs of a Schwarzschild black hole, the Reissner-Nordstrom QNMs are typically not periodic in the imaginary part of the frequency. This leads to the charged black hole having peculiar properties which complicate an interpretation of the results.