Exact Solutions of Regge-Wheeler Equation

TL;DR

This paper derives exact solutions to the Regge-Wheeler equation using confluent Heun's functions, providing new analytical and numerical methods to study black hole perturbations and quasi-normal modes.

Contribution

It introduces a novel analytical approach and numerical techniques for solving the Regge-Wheeler equation exactly, including solutions in complex geometries.

Findings

Exact solutions expressed via confluent Heun's functions.

Detailed solutions for Schwarzschild interior and Kruskal-Szekeres manifold.

Enhanced methods for analyzing black hole quasi-normal modes.

Abstract

The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic properties of the general solution, novel analytical approach and numerical techniques for study of different boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects. We depict in more detail the exact solutions of Regge-Wheeler equation in the Schwarzschild black hole interior and on Kruscal-Szekeres manifold.