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

Goedeke, Arne; Rendall, Alan D.

doi:10.1088/0264-9381/27/15/155019

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

MPS-Authors

Rendall, Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1002.1851
(Preprint), 201KB

CQG10_15_155019.pdf
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Citation

Goedeke, A., & Rendall, A. D. (2010). Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions. Classical and quantum gravity, 27(15): 155019. doi:10.1088/0264-9381/27/15/155019.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-6590-1

Abstract

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.