Birkhoff's theorem in Lovelock gravity

Zegers, Robin

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.

Citation

Zegers, R. (2005). Birkhoff's theorem in Lovelock gravity. Journal of Mathematical Physics, 46(7), Article 072502. https://doi.org/10.1063/1.1960798

• Journal Article Type: Article
• Acceptance Date: May 27, 2005
• Online Publication Date: Jul 15, 2005
• Publication Date: Jul 15, 2005
• Deposit Date: Feb 15, 2008
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 46
• Issue: 7
• Article Number: 072502
• DOI: https://doi.org/10.1063/1.1960798
• Publisher URL: http://arxiv.org/abs/gr-qc/0505016