Quasinormal modes and entropy spectrum of three dimensional Godel black hole

TL;DR

This paper analytically studies the quasinormal modes of scalar and spinor fields in a three-dimensional G"odel black hole, deriving their spectra and exploring implications for black hole entropy quantization.

Contribution

It provides exact solutions for wave equations and quasinormal modes in a G"odel black hole, linking these to entropy spectrum quantization, which is a novel analysis.

Findings

Quasinormal modes are exactly solvable using hypergeometric functions.

Transition frequencies are consistent across scalar and spinor fields.

Entropy spectrum of the G"odel black hole is equally spaced.

Abstract

We have studied perturbations of scalar and spinor field in the background of three dimensional G\"{o}del black hole. The wave equations are shown to be exactly solvable in terms of hypergeometric functions. The quasinormal modes are analytically calculated by imposing the Dirichlet boundary condition at spatial infinity, which are shown to be of the same form in both cases. By considering the physical interpretation of quasinormal modes, we obtain the consistent transition frequencies from the quasinormal modes of scalar and spinor field. As an application of quasinormal modes, we have also investigated the area and entropy quantization of three dimensional G\"{o}del black hole. By choosing the conserved mass of G\"{o}del black hole properly, the entropy spectrum are shown to be equally-spaced.