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  Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

Ehlers, J., & Buchert, T. (1997). Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory. General Relativity and Gravitation, 29(6), 733-764. doi:10.1023/A:1018885922682.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A9B-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A9C-D
Genre: Journal Article

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330685.pdf (Publisher version), 342KB
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 Creators:
Ehlers, Jürgen1, Author
Buchert, Thomas, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: 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.

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 Dates: 1997-06
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: eDoc: 330685
DOI: 10.1023/A:1018885922682
 Degree: -

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Title: General Relativity and Gravitation
  Alternative Title : GRG
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 29 (6) Sequence Number: - Start / End Page: 733 - 764 Identifier: ISSN: 0001-7701
ISSN: 1572-9532