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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)