Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects

TL;DR

This paper provides exact solutions to the Regge-Wheeler equation using recent mathematical methods, introduces new analytical and numerical techniques for studying quasi-normal modes of black holes and compact objects.

Contribution

It offers the first exact solutions of the Regge-Wheeler equation and develops novel analytical and numerical methods for analyzing quasi-normal modes.

Findings

Exact solutions of the Regge-Wheeler equation obtained.

New analytical approach for boundary problems.

Numerical techniques for quasi-normal modes developed.

Abstract

The well-known Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A novel analytical approach and numerical techniques for study the boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects are developed.