Quasi normal modes and the area spectrum of a near extremal de Sitter black hole with conformally coupled scalar field

TL;DR

This paper analyzes the quasi-normal modes of a near-extremal de Sitter black hole with a conformally coupled scalar field, deriving exact frequencies, comparing approximation methods, and establishing an equally spaced area spectrum.

Contribution

It provides exact quasi-normal mode frequencies for the MTZ black hole and demonstrates the area spectrum is equally spaced using a modified Hod's approach.

Findings

Exact QNM frequencies obtained for the MTZ black hole.

Comparison between 6th order WKB and exact methods shows good agreement.

The area spectrum is found to be equally spaced.

Abstract

In this paper we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the $MTZ$ black hole. We have obtained exact values for the quasi normal mode frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schr$\ddot{o}$dinger type equation with the well known P$\ddot{o}$shler-Teller potential. We have also used 6th order WKB approximation to compute quasinormal mode frequencies to compare with exact values obtained via the P$\ddot{o}$shler-Tell method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.