Generalized Kerr-NUT-de Sitter metrics in all dimensions

TL;DR

This paper classifies a broad class of higher-dimensional spacetimes with specific symmetries, generalizing known solutions like Kerr-NUT-de Sitter, and explicitly solves Einstein's equations for these metrics.

Contribution

It provides a complete classification of spacetimes with a closed conformal Killing-Yano tensor and explicitly solves the Einstein equations for these generalized metrics.

Findings

Explicit form of the Einstein metrics as indefinite integrals

Characterization of metrics by a polynomial in the integrand

Discussion of smoothness conditions on compact manifolds

Abstract

We classify all spacetimes with a closed rank-2 conformal Killing-Yano tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness conditions of the Einstein metrics over compact Riemannian manifolds.