Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions

Details Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions

2010-02-09

arxiv.org/abs/1002.1851v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages

Scientific paper

It is known that all spatially homogeneous solutions of the vacuum Einstein equations in four dimensions which exist for an infinite proper time towards the future are future geodesically complete. This paper investigates whether the analogous statement holds in higher dimensions. A positive answer to this question is obtained for a large class of models which can be studied with the help of Kaluza-Klein reduction to solutions of the Einstein-scalar field equations in four dimensions. The proof of this result makes use of a criterion for geodesic completeness which is applicable to more general spatially homogeneous models.

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