Integrability and the Kerr-(A)dS black hole in five dimensions

TL;DR

This paper demonstrates the separability of the Hamilton-Jacobi and Klein-Gordon equations in the five-dimensional Kerr-(A)dS black hole, revealing an irreducible Killing tensor and discussing broader implications.

Contribution

It proves the separability of key equations in five-dimensional Kerr-(A)dS spacetime and identifies an irreducible Killing tensor, advancing understanding of higher-dimensional black hole symmetries.

Findings

Hamilton-Jacobi equation is separable for arbitrary rotation parameters

Klein-Gordon equation is separable in this background

An irreducible Killing tensor is found

Abstract

In this note we prove that the Hamilton-Jacobi equation for a particle in the five dimensional Kerr-(A)dS black hole is separable, for arbitrary rotation parameters. As a result we find an irreducible Killing tensor. We also consider the Klein-Gordon equation in this background and show that this is also separable. Finally we comment on extensions and implications of these results.