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

Goedeke, Arne; Rendall, Alan D.

doi:http://dx.doi.org/10.1088/0264-9381/27/15/155019

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学術論文

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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フルテキスト (公開)

1002.1851
(プレプリント), 201KB

CQG10_15_155019.pdf
(全文テキスト（全般）), 137KB

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引用

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):. doi:http://dx.doi.org/10.1088/0264-9381/27/15/155019.

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

要旨

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.