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ID: 60186.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
Asymptotics of solutions of the Einstein equations with positive cosmological constant
Authors:Rendall, Alan D.
Language:English
Date of Publication (YYYY-MM-DD):2004
Title of Journal:Annales Henri Poincare
Volume:5
Issue / Number:6
Start Page:1041
End Page:1064
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
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