A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics

Abstract

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous characterization of the Kerr and Kerr-NUT metrics. The method of proof is based on (i) the presence of a second Killing vector field which is built in terms of geometric information arising from the previous Killing vector exclusively, and (ii) the existence of an interesting underlying geometric structure involving a Riemannian submersion of a conformally related metric, both of which may be of independent interest.

43 pages. No figures. v2: Statement of main theorem added in the Introduction. Section 4 divided into subsections. Minor additional changes. v3: Theorems 1 and 6 corrected to include a hypothesis that was not made explicit in version v1 and v2 and in the published paper. Relevant changes are highlighted in blue color. Some typos also amended