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

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-tri...

Full description

Saved in:
Bibliographic Details
Published inPhysics letters. B Vol. 609; no. 1-2; pp. 124 - 132
Main Authors Chong, Z.-W., Gibbons, G.W., Lü, H., Pope, C.N.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 03.03.2005
Elsevier Science
Subjects
Exact sciences and technology
Physics
The physics of elementary particles and fields
Kerr metric
Separability
De Sitter metric
Wave equations
Angular momentum
Compact manifold
Einstein manifold
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2004.07.066