Quasinormal frequencies of a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory

TL;DR

This paper numerically computes the quasinormal frequencies of Klein-Gordon and Dirac fields in a two-dimensional anti-de Sitter black hole within dilaton gravity, confirming stability and comparing spectra using multiple methods.

Contribution

It introduces a new approach for calculating Dirac quasinormal modes using coupled first order differential equations and compares results with established methods.

Findings

Quasinormal modes are stable for both fields.

Results from different numerical methods are consistent.

The spectra of Klein-Gordon and Dirac fields are analyzed for isospectrality.

Abstract

We numerically calculate the quasinormal frequencies of the Klein-Gordon and Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory. For the Klein-Gordon field we use the Horowitz-Hubeny method and the asymptotic iteration method for second order differential equations. For the Dirac field we first exploit the Horowitz-Hubeny method. As a second method, instead of using the asymptotic iteration method for second order differential equations, we propose to take as a basis its formulation for coupled systems of first order differential equations. For the two fields we find that the results that produce the two numerical methods are consistent. Furthermore for both fields we obtain that their quasinormal modes are stable and we compare their quasinormal frequencies to analyze whether their spectra are isospectral. Finally we discuss the main results.