Quasinormal modes of charged fields around a Reissner-Nordstr\"om black hole

TL;DR

This paper investigates the quasinormal modes of charged Dirac fields around Reissner-Nordström black holes, extending previous scalar field studies, deriving analytical formulas, and analyzing the impact of black hole charge and electromagnetic interaction.

Contribution

It introduces an analysis of Dirac fields' quasinormal modes around charged black holes, including an analytical formula for large electromagnetic interaction and comparison with scalar field results.

Findings

Imaginary part of frequencies approaches zero near extremal charge for charged fields.

Derived analytical formula for quasinormal frequencies at large electromagnetic interaction.

Compared Dirac and scalar field quasinormal modes, highlighting differences in behavior.

Abstract

The quasinormal spectrum of a charged scalar field around a non-extremal Reissner-Nordstr\"om black hole, specially in the limit of large electromagnetic interaction, has been comprehensively studied only very recently. In this work, we extend the analysis to Dirac fields using the continued fraction method and compare the results with the scalar case. In particular, we study the behaviour of the fundamental quasinormal mode as a function of the black hole's charge and of the electromagnetic interaction parameter. We derive an analytical formula for the quasinormal frequencies in the limit of large electromagnetic interaction. As the extremal limit of black hole charge is approached, we show that, unlike the case of neutral fields, the imaginary part of the quasinormal frequencies approach zero for charged fields.