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  Linear perturbations of spatially locally homogeneous spacetimes

Tanimoto, M. (2003). Linear perturbations of spatially locally homogeneous spacetimes. Contemporary Mathematics / AMS, 337, 171-185.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-532E-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-532F-1
Genre: Journal Article

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59725.pdf (Preprint), 249KB
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 Creators:
Tanimoto, Masayuki1, 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: Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston's H^2 x R) type, while the other is the Bianchi II (Thurston's Nil) type. With a brief summary of previous results on the Bianchi III perturbations, asymptotic solutions for the gauge-invariant variables for the Bianchi III are shown, with which (in)stability of the background solution is also examined. The issue of linear stability for a Bianchi II solution is still an open problem. To approach it, appropriate eigenfunctions are presented for an explicitly compactified Bianchi II manifold and based on that, some field equations on the Bianchi II background spacetime are studied. Differences between perturbation analyses for Bianchi class B (to which Bianchi III belongs) and class A (to which Bianchi II belongs) are stressed for an intention to be helpful for applications to other models.

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Language(s): eng - English
 Dates: 2003
 Publication Status: Published in print
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 Identifiers: eDoc: 59725
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Title: Contemporary Mathematics / AMS
Source Genre: Journal
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Pages: - Volume / Issue: 337 Sequence Number: - Start / End Page: 171 - 185 Identifier: -