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

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arxiv hep-th/0405061 v2 pith:6HBIBW2B submitted 2004-05-07 hep-th math.DG

Z.-W. Chong , G.W. Gibbons , H. Lu , C.N. Pope This is my paper · ORCID
classification hep-thmath.DG
keywords metricssitterarbitrarychargeclassdimensionskerr-dekerr-taub-nut-de
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Newman-Janis Algorithm from Taub-NUT Instantons

    gr-qc 2024-12 conditional novelty 7.0 of 10

    The Kerr metric is shown to be the exact nonlinear superposition of two Taub-NUT instantons of opposite chirality, explaining the Newman-Janis algorithm.

  2. Pleba\'nski-Demia\'nski solutions in bigravity and Kerr-Schild double copy relations using an effective metric

    gr-qc 2024-12 conditional novelty 5.0 of 10

    A double Kerr-Schild ansatz in bigravity yields Plebanski-Demianski-type solutions whose double, single, and zeroth copy fields satisfy Maxwell and Klein-Gordon equations in Plebanski coordinates.

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