Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime

TL;DR

This paper classifies higher-dimensional spacetimes with a rank-2 closed conformal Killing-Yano tensor, establishing the uniqueness of the Kerr-NUT-de Sitter spacetime as the only non-degenerate case, thus generalizing its geometric properties.

Contribution

It provides a classification of spacetimes with a rank-2 closed CKY tensor, proving the Kerr-NUT-de Sitter spacetime's uniqueness among them.

Findings

Kerr-NUT-de Sitter spacetime admits a non-degenerate CKY tensor.

It is the only spacetime with such a tensor.

The classification generalizes known symmetries of black hole solutions.

Abstract

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a non-degenerate CKY tensor.