BTZ quasinormal frequencies as poles of Green's function

TL;DR

This paper presents a method to exactly compute the quasinormal frequencies of the Klein-Gordon field in a 3D rotating BTZ black hole, leveraging their relation to Green's function poles, with potential applications to other backgrounds.

Contribution

It introduces a new exact computational method for quasinormal frequencies based on Green's function poles, demonstrated on the BTZ black hole.

Findings

Exact quasinormal frequencies calculated for the Klein-Gordon field in BTZ black hole

Method shows potential for application to other classical fields and backgrounds

Comparison with previous results validates the approach

Abstract

Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green's function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating BTZ black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.