On the existence of \(n\)-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure
type: Item
instance of: scholarly article
title: On the existence of \(n\)-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure
zbMATH Open document ID: 0659.53056
DOI: 10.1007/BF01205488
author: Helmut Friedrich
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: It is demonstrated that initial data sufficiently close to de-Sitter data develop into solutions of Einstein's equations \(\text{Ric}[g]=\Lambda g\) with positive cosmological constant \(\Lambda\), which are asymptotically simple in the past as well as in the future, whence null geodesically complete. Furthermore it is shown that hyperboloidal initial data (describing hypersurfaces which intersect future null infinity in a space-like two- sphere), which are sufficiently close to Minkowskian hyperboloidal data, develop into future asymptotically simple whence null geodesically future complete solutions of Einstein's equations \(\text{Ric}[g]=0\), for which future null infinity forms a regular cone with vertex \(i^+\) that represents future time-like infinity.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 4078207
zbMATH Keywords: Einstein's equations
zbMATH Keywords: hyperboloidal initial data
zbMATH Keywords: null geodesically future complete solutions
zbMATH Keywords: null infinity
zbMATH Keywords: future time-like infinity
MaRDI profile type: Publication
cites work: Q4073917
cites work: Singular perturbation and boundary layer for an abstract Cauchy problem
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: On the existence of analytic null asymptotically flat solutions of Einstein’s vacuum field equations
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: Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant
cites work: The Large Scale Structure of Space-Time
cites work: Q5627250
cites work: Linear evolution equations of ''hyperbolic'' type. II
cites work: The Cauchy problem for quasi-linear symmetric hyperbolic systems
full work available at URL: https://doi.org/10.1007/bf01205488
OpenAlex ID: W2035054911
Wikidata QID: Q125878767
description: scientific article; zbMATH DE number 4078207