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

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.Comment: 13 pages; v2: title amended, to be published in Classical and Quantum Gravit

The Einstein static universe in Loop Quantum Cosmology

Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.Comment: 12 pages, 7 figures; v2: minor changes to match published version in Classical and Quantum Gravit