Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime

TL;DR

This paper proves that spacetimes with a principal conformal Killing-Yano tensor are uniquely described by the Kerr-NUT-(A)dS metric in higher dimensions, and such symmetries imply integrability and separability properties.

Contribution

It establishes the uniqueness of the Kerr-NUT-(A)dS solution among Einstein spacetimes with hidden symmetries in higher dimensions.

Findings

The Kerr-NUT-(A)dS metric is the most general Einstein solution with a principal conformal Killing-Yano tensor.

Spacetimes with such hidden symmetries are Petrov type D.

Geodesic motion and wave equations are separable and integrable in these spacetimes.

Abstract

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.