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          Institute: MPI für Gravitationsphysik     Collection: Geometric Analysis and Gravitation     Display Documents



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ID: 330685.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
Authors:Ehlers, Jürgen; Buchert, Thomas
Date of Publication (YYYY-MM-DD):1997-06
Title of Journal:General Relativity and Gravitation
Journal Abbrev.:GRG
Volume:29
Issue / Number:6
Start Page:733
End Page:764
Review Status:not specified
Abstract / Description:The ldquoNewtonianrdquo theory of spatially unbounded, self-gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space R3 from closed models based (without loss of generality) on a flat torus T3. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous ldquobackgroundrdquo model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:ISSN:0001-7701 [Print]
ISSN:1572-9532 [Online]
DOI:10.1023/A:1018885922682
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