Elliptic-hyperbolic systems and the Einstein equations

Lars Andersson; Vincent Moncrief

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arXiv · gr-qc/0110111

Elliptic-hyperbolic systems and the Einstein equations

Lars Andersson·Vincent Moncrief

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Abstract

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution equations. We 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 spacetimes.

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Lars Andersson, Vincent Moncrief. 2002-02-21. Elliptic-hyperbolic systems and the Einstein equations. https://arxiv.org/abs/gr-qc/0110111

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