On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case

Details On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case

2007-12-21

arxiv.org/abs/0712.3758v2

Class.Quant.Grav.25:165016,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages; v2: title amended, to be published in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/25/16/165016

The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, 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 space-time is related to the degenerated horizon metric of certain black-hole space-times of the allowed class. This result resembles the connection between the Bertotti-Robinson space-time and the horizon region of the extremal Reissner-Nordstrom space-time in general relativity.

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