The general Kerr-de Sitter metrics in all dimensions Academic Article

abstract

• We give the general Kerr-de Sitter metric in arbitrary space-time dimension D 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 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 SD-2 bundles over S2, infinitely many for each odd D 5. 2004 Published by Elsevier B.V.

authors

• Pope, Christopher

published proceedings

• JOURNAL OF GEOMETRY AND PHYSICS

author list (cited authors)

• Gibbons, G. W., Lu, H., Page, D. N., & Pope, C. N.

citation count

• 335

publication date

• January 2005

publisher

• Elsevier  Publisher

published in

• Journal of Geometry and Physics  Journal

keywords

• Compact Einstein Spaces
• Kerr-de Sitter Metrics

Digital Object Identifier (DOI)

• 10.1016/j.geomphys.2004.05.001

start page

• 49

end page

• 73

volume

• 53

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.geomphys.2004.05.001