Properties of a model Einstein equation
type: Item
instance of: scholarly article
title: Properties of a model Einstein equation
zbMATH Open document ID: 0707.35150
DOI: 10.1007/BF00755984
author: Roger Ove
published in: General Relativity and Gravitation
publication date: 1990-01-01T00:00:00Z
review text: Although chaos is almost a generally property of nonlinear systems of equations its existence in the case of the solution of Einstein's equations is still an open question. The author, starting from the Einstein equations on \(T^ 3\times {\mathbb{R}}\) with one Killing vector, makes a series of justified approximations and develops a nice toy model to analyse using numerical methods, the chaotic behavior of the vacuum-type solutions for a closed space-time with a Killing vector symmetry. An exact solution exhibits chaos if its behavior for smooth initial data, mixes the Fourier decomposition modes and presents an exponential phase-space expansion. The author's conclusions are: chaos is highly correlated with gravitational radiation emitted by unstables smooth regions of the universe, some regions which expands faster than the rest of the universe exhibit chaos and chaos is a physical consequence of the space time singularities or (more interesting) vice versa.
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 4161313
zbMATH Keywords: chaos
zbMATH Keywords: Einstein's equations
zbMATH Keywords: Einstein equations
zbMATH Keywords: model
zbMATH Keywords: vacuum-type solutions
reviewed by: Ciprian Dariescu
MaRDI profile type: Publication
cites work: Reduction of Einstein's equations for vacuum space-times with spacelike U(1) isometry groups
cites work: A Method for Generating Solutions of Einstein's Equations
cites work: A Method for Generating New Solutions of Einstein's Equation. II
cites work: Electrostatic forces and shadow effects in planetary dust rings
cites work: Chaos in the long-term behavior of some Bianchi-type VIII models
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description: scientific article; zbMATH DE number 4161313