Quasinormal modes of nearly extreme Reissner-Nordstrom black holes

TL;DR

This paper provides detailed calculations of quasinormal modes of Reissner-Nordstrom black holes, revealing how modes depend on charge and identifying peculiar features of rapidly damped modes, including potential new modes.

Contribution

It offers new insights into the behavior of quasinormal modes for charged black holes, especially near extremality, and suggests the existence of a purely imaginary mode in Schwarzschild black holes.

Findings

Higher modes spiral into the extremal black hole value as charge increases.

Rapidly damped modes exhibit peculiar features not seen in slowly damped modes.

Evidence suggests a purely imaginary mode approaching a -2i for Schwarzschild black holes.

Abstract

We present detailed calculations of the quasinormal modes of Reissner-Nordstrom black holes. While the first few, slowly damped, modes depend on the charge of the black hole in a relatively simple way, we find that the rapidly damped modes show several peculiar features. The higher modes generally spiral into the value for the extreme black hole as the charge increases. We also discuss the possible existence of a purely imaginary mode for the Schwarzschild black hole: Our data suggest that there is a quasinormal mode that limits to $\omega M = -2i$ as $Q\to 0$.