Kerr-de Sitter Black Holes with NUT Charges

TL;DR

This paper extends Kerr-AdS black hole solutions to include NUT charges in higher dimensions, explores their supersymmetric limits, and reveals coordinate transformations linking over-rotating and under-rotating metrics.

Contribution

It introduces a generalization of higher-dimensional Kerr-AdS metrics with NUT parameters and analyzes their properties, including supersymmetric limits and Euclidean counterparts.

Findings

Higher-dimensional Kerr-AdS metrics admit NUT-type generalizations.

Euclidean versions yield new Einstein-Sasaki and Ricci-flat metrics.

Coordinate transformations relate over-rotating and under-rotating five-dimensional Kerr-AdS metrics.

Abstract

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.