Kerr–de Sitter black holes with NUT charges

The four-dimensional Kerr–de Sitter and Kerr–AdS black hole metrics have cohomogeneity 2, and they admit a generalisation in which an additional parameter characterising a NUT charge is included. In this paper, we study the higher-dimensional Kerr–AdS metrics, specialised to cohomogeneity 2 by appropriate restrictions on their rotation parameters, and we show how they too admit a generalisation in which an additional NUT-type parameter is introduced. We discuss also the supersymmetric limits of the new metrics. If one performs a Wick rotation to Euclidean spacetime signature, these yield new Einstein–Sasaki metrics in odd dimensions, and Ricci-flat metrics in even dimensions. We also study the five-dimensional Kerr–AdS black holes in detail. Although in this particular case the NUT parameter is trivial, our investigation reveals the remarkable feature that a five-dimensional Kerr–AdS “over-rotating” metric is equivalent, after performing a coordinate transformation, to an under-rotating Kerr–AdS metric.