Birkhoff's theorem in Lovelock gravity

Details Birkhoff's theorem in Lovelock gravity Birkhoff's theorem in Lovelock gravity

2005-05-03

arxiv.org/abs/gr-qc/0505016v1

J.Math.Phys.46:072502,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

10.1063/1.1960798

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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