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.
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