Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
arXiv:hep-th/0405061 · doi:10.1016/j.physletb.2004.07.066
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.
Author added, title changed, references added, focus of paper changed to Killing tensors and separability. Latex, 13 pages
References in corpus (5)
- Rotation and the AdS/CFT correspondence
- The General Kerr-de Sitter Metrics in All Dimensions
- Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
- Rotating Black Branes wrapped on Einstein Spaces
- New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes
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- The classical double copy for Taub-NUT spacetime
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- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
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- Killing(-Yano) Tensors in String Theory
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- A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
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- Integrability of Some Charged Rotating Supergravity Black Hole Solutions in Four and Five Dimensions
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- Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group of motions
- Single-rotation two-charge black holes in gauged supergravity
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