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

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.