Separability and Killing tensors in Kerr–Taub-NUT–de Sitter metrics in higher dimensions

Abstract

A generalisation of the four-dimensional Kerr–de Sitter metrics to include a NUT charge is well known, and is included within a class of metrics obtained by Plebanski. In this Letter, we study a related class of Kerr–Taub-NUT–de Sitter metrics in arbitrary dimensions D⩾6, which contain three non-trivial continuous parameters, namely the mass, the NUT charge, and a (single) angular momentum. We demonstrate the separability of the Hamilton–Jacobi and wave equations, we construct a closely-related rank-2 Stäckel–Killing tensor, and we show how the metrics can be written in a double Kerr–Schild form. Our results encompass the case of the Kerr–de Sitter metrics in arbitrary dimension, with all but one rotation parameter vanishing. Finally, we consider the real Euclidean-signature continuations of the metrics, and show how in a limit they give rise to certain recently-obtained complete non-singular compact Einstein manifolds.