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  Asymptotics of solutions of the Einstein equations with positive cosmological constant

Rendall, A. D. (2004). Asymptotics of solutions of the Einstein equations with positive cosmological constant. Annales Henri Poincare, 5(6), 1041-1064.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-50DF-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-50E0-5
Genre: Journal Article

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60186.pdf (Preprint), 258KB
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Rendall, Alan D.1, 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: A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum spacetimes of any dimension and perfect fluid spacetimes with linear equation of state in spacetime dimension four. For equations of state stiffer than radiation evidence for development of large gradients, analogous to spikes in Gowdy spacetimes, is found. It is shown that any vacuum solution satisfying minimal asymptotic conditions has a full asymptotic expansion given by the formal series. In four spacetime dimensions, and for spatially homogeneous spacetimes of any dimension, these minimal conditions can be derived for appropriate initial data. Using Fuchsian methods the existence of vacuum spacetimes with the given formal asymptotics depending on the maximal number of free functions is shown without symmetry assumptions.

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Language(s): eng - English
 Dates: 2004
 Publication Status: Published in print
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 Identifiers: eDoc: 60186
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Title: Annales Henri Poincare
Source Genre: Journal
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Pages: - Volume / Issue: 5 (6) Sequence Number: - Start / End Page: 1041 - 1064 Identifier: -