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arXiv · 1307.5018

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

Marc Mars·José M. M. Senovilla
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Abstract

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-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.

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Marc Mars, José M. M. Senovilla. 2013-07-18. A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics. https://arxiv.org/abs/1307.5018

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