On the hyperbolicity of Einstein's and other gauge field equations
type: Item
instance of: scholarly article
title: On the hyperbolicity of Einstein's and other gauge field equations
zbMATH Open document ID: 0588.35058
DOI: 10.1007/BF01217728
author: Helmut Friedrich
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: It is shown that gauge field equations, including the Yang-Mills and Einstein's field equations, if suitably understood imply symmetric hyperbolic systems of propagation equations for any choice of gauge. In the equations appear certain freely specifiable ''gauge source functions'', which govern the propagation of the gauge off a suitable initial surface. The method is discussed in detail for the ''regular conformal field equations'' for the conformally rescaled metric field in general relativity. Besides the coordinate and the frame gauge source functions may be given here arbitrarily the Ricci-scalar which constitutes the gauge source function which determines the propagation of the conformal factor. The technique has been applied to analyse the existence of radiative space-times by the author [''On Purely Radiative Space-Times'', ibid. 103, 35-65 (1986)]. Furthermore it led to the first general results on the global existence and the asymptotic behaviour of solutions of Einstein's field equations with positive cosmological constant [see the author, ''On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure''. Preprint, Hamburg (1986)].
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C30
Mathematics Subject Classification ID: 58J45
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3944407
zbMATH Keywords: gauge field equations
zbMATH Keywords: Einstein's field equations
zbMATH Keywords: symmetric hyperbolic systems
zbMATH Keywords: propagation equations
zbMATH Keywords: regular conformal field equations
zbMATH Keywords: existence of radiative space-times
MaRDI profile type: Publication
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 regular and the asymptotic characteristic initial value problem for Einstein’s vacuum field equations
cites work: Cauchy problems for the conformal vacuum field equations in general relativity
cites work: Symmetric hyperbolic linear differential equations
cites work: Q3280274
cites work: The Cauchy problem for quasi-linear symmetric hyperbolic systems
cites work: Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
cites work: Q5679204
full work available at URL: https://doi.org/10.1007/bf01217728
OpenAlex ID: W1979995289
Wikidata QID: Q126050797
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description: scientific article; zbMATH DE number 3944407