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.
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