The Goursat problem at the horizons for the Klein-Gordon equation on the De Sitter-Kerr metric

TL;DR

This paper addresses the Goursat problem at the horizons for the Klein-Gordon equation on the De Sitter-Kerr metric, providing solutions for small black hole angular momentum and fixed field angular momentum.

Contribution

It offers a novel solution to the Goursat problem in the context of the De Sitter-Kerr spacetime with small angular momentum.

Findings

Solved the Goursat problem for fixed angular momentum n

Established solutions for non-zero n in the massless case

Focused on the small angular momentum regime

Abstract

The main topic is the Goursat problem at the horizons for the Klein-Gordon equation on the De Sitter-Kerr metric when the angular momentum per unit of mass of the black hole is small. We solve the Goursat problem for fixed angular momentum n of the field (with the restriction that n is non zero in the case of a massless field).