On the validity of the five-dimensional Birkhoff theorem: The tale of an exceptional case

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Abstract

The five-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum spacetimes containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) spacetime, which is not a representant of the above class, but contains the static Einstein brane as embedded hypersurface. We prove that the 5d Birkhoff theorem is still satisfied in a weaker sense: the GM spacetime is related to the degenerated horizon metric of certain black hole spacetimes of the allowed class. This result resembles the connection between the Bertotti-Robinson spacetime and the horizon region of the extremal Reissner-Nordstrom spacetime in general relativity.

Original languageEnglish
Article number165016
JournalClassical and Quantum Gravity
Volume25
Issue number16
DOIs
Publication statusPublished - Aug 21 2008

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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