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High Energy Physics - Theory

arXiv:hep-th/0404008 (hep-th)
[Submitted on 1 Apr 2004 (v1), last revised 12 Aug 2004 (this version, v3)]

Title:The General Kerr-de Sitter Metrics in All Dimensions

Authors:G.W. Gibbons, H. Lu, D.N. Page, C.N. Pope
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Abstract: We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D\ge 4, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null geodesic vector, and in generalised Boyer-Lindquist coordinates. The Kerr-Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D\le 11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D \ge 5.
Comments: Latex, 27 pages, typos corrected, version to appear in J. Geom. Phys
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
Report number: DAMTP-2004-37, MIFP-04-07, Alberta Thy 07-04
Cite as: arXiv:hep-th/0404008
  (or arXiv:hep-th/0404008v3 for this version)
  https://doi.org/10.48550/arXiv.hep-th/0404008
Journal reference: J.Geom.Phys.53:49-73,2005
Related DOI: https://doi.org/10.1016/j.geomphys.2004.05.001

Submission history

From: Hong Lu [view email]
[v1] Thu, 1 Apr 2004 20:59:05 UTC (17 KB)
[v2] Wed, 5 May 2004 15:08:24 UTC (22 KB)
[v3] Thu, 12 Aug 2004 15:37:14 UTC (23 KB)
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