Rotating Black Holes in Higher Dimensions with a Cosmological Constant
G. W. Gibbons, H. Lu, D. N. Page, C. N. Pope
TL;DR
The metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions is presented and smooth compact Einstein spaces on associated S(D-2) bundles over S2 are obtained.
Abstract
We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.