Analytic solutions of the Regge-Wheeler equation and the Post-Minkowskian expansion

Abstract

Analytic solutions of the Regge-Wheeler equation are presented in the form of a series of hypergeometric functions and Coulomb wave functions which have different regions of convergence. Relations among these solutions are established. The series solutions are given as the Post-Minkowskian expansion with respect to the parameter ε=2Mω, M being the mass of a black hole. This expansion corresponds to the post-Newtonian expansion when they are applied to the gravitational radiation from a particle in a circular orbit around a black hole. These solutions can also be useful for numerical computations.