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  Future asymptotic expansions of Bianchi VIII vacuum metrics

Ringström, H. (2003). Future asymptotic expansions of Bianchi VIII vacuum metrics. Classical and Quantum Gravity, 20(11), 1943-1989.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-52DD-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-52DE-E
Genre: Journal Article

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50968.pdf (Preprint), 528KB
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 Creators:
Ringström, Hans1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: Bianchi VIII vacuum solutions to Einstein’s equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine. Finally, we give asymptotic expansions for general Bianchi VII0 metrics.

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Language(s): eng - English
 Dates: 2003
 Publication Status: Published in print
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 Identifiers: eDoc: 50968
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 20 (11) Sequence Number: - Start / End Page: 1943 - 1989 Identifier: -