The Quasinormal Modes and Isospectrality of Bardeen (Anti-) de Sitter Black Holes

TL;DR

This paper analyzes the quasinormal modes of Bardeen (Anti-) de Sitter black holes, revealing isospectrality breaking in de Sitter cases and providing numerical QNM calculations using WKB and HH methods.

Contribution

It derives master equations for gravitational perturbations of Bardeen (Anti-) de Sitter black holes and computes their quasinormal modes, highlighting differences in isospectrality.

Findings

Isospectrality is broken in Bardeen de Sitter black holes.

QNM frequencies are computed for both cases using numerical methods.

The study provides new insights into the stability and perturbation spectra of regular black holes.

Abstract

Black holes (BHs) exhibiting coordinate singularities but lacking essential singularities throughout the entire spacetime are referred to as regular black holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who considered the Einstein equation coupled with a nonlinear electromagnetic field. In this study, we investigate the gravitational perturbations, including the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We derive the master equations with source terms for both axial and polar perturbations, and subsequently compute the quasinormal modes (QNMs) through numerical methods. For the Bardeen de Sitter black hole, we employ the 6th-order WKB approach. The numerical results reveal that the isospectrality is broken in this case. Conversely, for Bardeen Anti-de Sitter black holes, the QNM frequencies are calculated by using the HH method.