Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics

TL;DR

This paper demonstrates that Hamilton-Jacobi and Klein-Gordon equations are separable in cohomogeneity-2 Kerr-AdS and NUT black hole backgrounds across all dimensions, revealing hidden symmetries via Killing tensors.

Contribution

It extends the separability property to higher-dimensional Kerr-AdS and NUT black holes with cohomogeneity 2, and constructs associated Killing tensors, generalizing previous results.

Findings

Separable equations in all dimensions for cohomogeneity-2 Kerr-AdS backgrounds

Existence of irreducible rank-2 Killing tensors indicating hidden symmetries

Connections between special cases and previous literature

Abstract

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all dimensions, if one specialises the rotation parameters so that the metrics have cohomogeneity 2. Furthermore, we show that this property of separability extends to the NUT generalisations of these cohomogeneity-2 black holes that we obtained in a recent paper. In all these cases, we also construct the associated irreducible rank-2 Killing tensor whose existence reflects the hidden symmetry that leads to the separability. We also consider some cohomogeneity-1 specialisations of the new Kerr-NUT-AdS metrics, showing how they relate to previous results in the literature.