Perturbations of Kerr-de Sitter black holes and Heun's equations

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 it has been thought that their analysis would be difficult. We show that these equations can be transformed into Heun's equations, for which we are able to use a known technique to analyze solutions. We reproduce known results for the Kerr geometry and de Sitter geometry in the confluent limits of Heun's functions. Our analysis can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and 1.2.