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Birkhoff's theorem in Lovelock gravity

Robin Zegers
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Abstract

We show that the generic solutions of the Lovelock equations with spherical, planar or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional Killing vector that can either be space-like or time-like, depending on the position. This result also holds in the presence of an abelian gauge field, in which case the solutions are locally isometric to a charged static black hole.

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Robin Zegers. 2005-05-03. Birkhoff's theorem in Lovelock gravity. https://doi.org/10.1063/1.1960798

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