Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions

TL;DR

This paper extends Kerr-Taub-NUT-de Sitter metrics to higher dimensions, demonstrating their separability, constructing associated Killing tensors, and exploring their geometric properties and limits.

Contribution

It introduces a class of higher-dimensional Kerr-Taub-NUT-de Sitter metrics with three parameters, showing their separability and geometric structures, including Killing tensors and Kerr-Schild forms.

Findings

Separable Hamilton-Jacobi and wave equations in these metrics

Construction of a rank-2 Staeckel-Killing tensor

Metrics can be expressed in double Kerr-Schild form

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 paper, we study a related class of Kerr-Taub-NUT-de Sitter metrics in arbitrary dimensions D \ge 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 Staeckel-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.