Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant
type: Item
instance of: scholarly article
title: Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant
zbMATH Open document ID: 0592.53061
DOI: 10.1016/0393-0440(86)90004-5
author: Helmut Friedrich
published in: Journal of Geometry and Physics
publication date: 1986-01-01T00:00:00Z
review text: The author exploits his earlier rewriting of the Einstein field equations in a conformal way [Commun. Math Phys. 100, 525-543 (1985; Zbl 0588.35058)] to analyse the initial value problem when the cosmological constant is positive, a case which is easier than the corresponding pure radiation problem with it zero. He uses these results to prove the conjecture that when a solution of this case has a time-like Killing vector field, then the metrics in the causal pasts of points in the conformally extended space-time are conformally flat.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C30
zbMATH DE Number: 3951509
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Einstein field equations
zbMATH Keywords: Killing vector field
zbMATH Keywords: conformally extended space-time
zbMATH Keywords: conformally flat
reviewed by: C. W. Kilmister
MaRDI profile type: Publication
full work available at URL: 0393-0440(86)90004-5
OpenAlex ID: W2087102109
cites work: Q3697760
cites work: Q3858873
cites work: The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system
cites work: Cauchy problems for the conformal vacuum field equations in general relativity
cites work: On the hyperbolicity of Einstein's and other gauge field equations
cites work: On purely radiative space-times
cites work: Symmetric hyperbolic linear differential equations
cites work: Domain of Dependence
cites work: The Measure of the Universe
cites work: The Large Scale Structure of Space-Time
cites work: The Cauchy problem for quasi-linear symmetric hyperbolic systems
cites work: An Approach to Gravitational Radiation by a Method of Spin Coefficients
cites work: Zero rest-mass fields including gravitation: asymptotic behaviour
cites work: Gravitational collapse: The role of general relativity
cites work: Differentiability of Solutions to Hyperbolic Initial Boundary Value Problems
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description: scientific article; zbMATH DE number 3951509