Perturbations of Kerr-de Sitter Black Hole and Heun's Equations

TL;DR

This paper demonstrates that perturbation equations for Kerr-de Sitter black holes can be transformed into Heun's equations, enabling the use of known analytical techniques and extending previous results to more complex geometries.

Contribution

The authors show how to convert Kerr-de Sitter perturbation equations into Heun's equations, facilitating analysis and extending results to Kerr-Newman-de Sitter geometries.

Findings

Reproduced known results for Kerr and de Sitter geometries

Extended analysis to Kerr-Newman-de Sitter geometry

Applied Heun's functions to black hole perturbation equations

Abstract

It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities so that the analysis has been expected to be difficult. We show that these equations can be transformed to Heun's equations, for which we are able to use known technique for the analysis of the solutions. We reproduce results known previously for the Kerr geometry and de Sitter geometry in the confluent limits of the Heun's functions. Our analysis applies can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and 1/2.