Quasinormal modes of maximally charged black holes

TL;DR

This paper introduces a new, highly precise algorithm for calculating quasinormal frequencies of extremal Reissner-Nordström black holes, confirming previous results and revealing a surprising frequency coincidence between gravitational and electromagnetic waves.

Contribution

A novel algorithm for accurately computing quasinormal modes of extremal black holes, improving precision over existing methods.

Findings

Computed quasinormal frequencies align with previous results.

Discovered that gravitational and electromagnetic wave frequencies coincide in the extremal limit.

Enhanced accuracy of quasinormal mode calculations.

Abstract

A new algorithm for computing the accurate values of quasinormal frequencies of extremal Reissner-Nordstr\"{o}m black holes is presented. The numerically computed values are consistent with the values earlier obtained by Leaver and those obtained through the WKB method. Our results are more precise than other results known to date. We also find a curious fact that the resonant frequencies of gravitational waves with multi-pole index $l$ coincide with those of electromagnetic waves with multi-pole index $l-1$ in the extremal limit.