Elliptic-hyperbolic systems and the Einstein equations
type: Item
instance of: scholarly article
title: Elliptic-hyperbolic systems and the Einstein equations
zbMATH Open document ID: 1028.83005
author: Lars Andersson
author: Vincent Moncrief
published in: Annales Henri Poincaré
publication date: 2003-07-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/gr-qc/0110111
review text: The authors of this interesting paper study the Einstein equations in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasi-linear elliptic-hyperbolic system of evolution equations. The hyperbolic part of this system is a modified version of the Einstein evolution equations, and the elliptic part consists of the defining equations for lapse and shift. The authors prove that the Cauchy problem is locally strongly well posed and that a continuation principle holds. For initial data satisfying the Einstein constraint and gauge conditions, the solutions to the elliptic-hyperbolic system defined by the gauge fixed Einstein evolution equations are shown to give vacuum space-times.
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 35M10
zbMATH DE Number: 1945920
zbMATH Keywords: elliptic-hyperbolic system
zbMATH Keywords: Einstein equations
zbMATH Keywords: gauge
zbMATH Keywords: Cauchy problem
reviewed by: Dimitar A. Kolev
MaRDI profile type: Publication
OpenAlex ID: W2073243744
arXiv ID: gr-qc/0110111
DOI: 10.1007/S00023-003-0120-1
description: scientific article