Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times
type: Item
instance of: scholarly article
title: Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times
zbMATH Open document ID: 0840.53055
DOI: 10.1016/0393-0440(94)00042-3
author: Helmut Friedrich
published in: Journal of Geometry and Physics
publication date: 1996-06-30T00:00:00Z
full work available at URL: 00-001M-0000-0013-5B83-C
review text: The author develops and discusses in detail the conformal structure of space-time and, in particular, of the Einstein equations. By conformal extension, a space-time can aquire a boundary, so that asymptotic conditions become boundary conditions. Cauchy's problem to Einstein's equations is treated as an initial and boundary value problem. The author proves a theorem of existence and uniqueness of a global solution which he calls of ``anti-de Sitter type'' because of some likeness to the anti-de Sitter space-time. This type is asymptotically simple and has a positive cosmological constant. The analytical tools come from a paper of \textit{O. Guès} of 1990.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 83C15
zbMATH DE Number: 816010
zbMATH Keywords: Cauchy problem
zbMATH Keywords: conformal structure
zbMATH Keywords: Einstein equations
zbMATH Keywords: conformal extension
reviewed by: Rainer Schimming
MaRDI profile type: Publication
OpenAlex ID: W2154157974
cites work: On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
cites work: On the existence of \(n\)-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure
cites work: On static and radiative space-times
cites work: On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations
cites work: Conformal geodesics in general relativity
cites work: Probleme Mixte Hyperbolique Quasi-Lineaire Caracteristique
cites work: The Large Scale Structure of Space-Time
cites work: Asymptotically anti-de Sitter spaces
cites work: Q5658761
cites work: Theory of conformal connections
cites work: Q5527788
cites work: Zero rest-mass fields including gravitation: asymptotic behaviour
cites work: Gravitational collapse: The role of general relativity
cites work: Q3719405
cites work: Symmetric Positive Systems with Boundary Characteristic of Constant Multiplicity
cites work: Pseudodifferential operators and nonlinear PDE
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description: scientific article; zbMATH DE number 816010