Quasinormal Modes of Extremal BTZ Black Hole

TL;DR

This paper calculates quasinormal modes of extremal BTZ black holes, showing that their frequencies have zero imaginary part, indicating non-dissipative modes, and provides exact results for scalar and fermionic perturbations.

Contribution

It explicitly computes quasinormal modes for extremal BTZ black holes, demonstrating their non-dissipative nature and establishing bounds for normal mode existence.

Findings

Imaginary part of frequency is zero for extremal BTZ black holes.

Exact solutions obtained for scalar and fermionic perturbations.

Frequency is bounded from below for normal modes.

Abstract

Motivated by several pieces of evidence, in order to show that extreme black holes cannot be obtained as limits of non-extremal black holes, in this article we calculate explicitly quasinormal modes for Ba\~{n}ados, Teitelboim and Zanelli (BTZ) extremal black hole and we showed that the imaginary part of the frequency is zero. We obtain exact result for the scalar an fermionic perturbations. We also showed that the frequency is bounded from below for the existence of the normal modes (non-dissipative modes).