A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

TL;DR

This paper demonstrates that higher-dimensional Kerr-AdS black holes with NUT charge admit a Killing tensor, enabling the separation of variables in geodesic and scalar field equations, thus proving their integrability.

Contribution

It introduces a new Killing tensor for these black holes, establishing their geodesic and scalar field separability, which was previously unknown.

Findings

Existence of an irreducible Killing tensor.

Separable Hamilton-Jacobi equation.

Separable Klein-Gordon equation.

Abstract

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable.