The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes

TL;DR

This paper investigates the highly damped quasinormal modes of extremal Reissner-Nordström and Reissner-Nordström-de Sitter black holes, revealing that their frequencies match the extremal limit of non-extremal cases despite topological differences.

Contribution

It provides a detailed analysis showing the consistency of quasinormal mode frequencies in extremal black holes with the extremal limit of non-extremal black holes, despite topological differences.

Findings

Extremal black hole QNM frequencies match the extremal limit of non-extremal frequencies.

Topology of Stokes/anti-Stokes lines differs between extremal and non-extremal cases.

The analysis confirms the robustness of QNM frequency predictions across extremal limits.

Abstract

We analyze in detail the highly damped quasinormal modes of $D$-dimensional extremal Reissner-Nordstr$\ddot{\rm{o}}$m and Reissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.