The general Kerr–de Sitter metrics in all dimensions
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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.
author list (cited authors)
Gibbons, G. W., Lü, H., Page, D. N., & Pope, C. N.