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.