The general Kerr-de Sitter metrics in all dimensions

We give the general Kerr-de Sitter metric in arbitrary space-time dimension D > 4, with the maxima. 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 S-2, infinitely many for each odd D greater than or equal to 5. (C) 2004 Published by Elsevier B.V.