New solutions of Radial Teukolsky Equation via transformation to Heuns Equation with the application of rational polynomial of at most degree 2, 3, 4, 5, 6

Abstract

The perturbation equation of masseless fields for Kerr-de Sitter geometry are written in form of seperable equations called the Radial Teukolsky equation. The Angular Teukolsky equation is converted to General Heun's equationwith singularities coinciding through some confluent process of one of five singularities. As in [4, 16, 17] rational polynomials of at most degree six are introduced.