Birkhoff theorem and conformal Killing-Yano tensors

Abstract

We analyze the main geometric conditions imposed by the hypothesis of the Jebsen-Birkhoff theorem. We show that the result (existence of an additional Killing vector) does not necessarily require a three-dimensional isometry group on two-dimensional orbits but only the existence of a conformal Killing-Yano tensor. In this approach the (additional) isometry appears as the known invariant Killing vector that the $\mathcal{D}$-metrics admit.

7 pages; accepted in General Relativity and Gravitation

References in corpus (1)

• On the invariant symmetries of the $\mathcal{D}$-metrics

Cited by in corpus (1)

• Geometrical origin of the Kodama vector