A non-strictly hyperbolic system for the Einstein equations with arbitrary lapse and shift

Details A non-strictly hyperbolic system for the Einstein equations with arbitrary lapse and shift A non-strictly hyperbolic system for the Einstein equations with arbitrary lapse and shift

1996-07-03

arxiv.org/abs/gr-qc/9607006v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pp., LaTeX

Scientific paper

We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the normal to the slice for any choice of lapse and shift functions, and it admits a well-posed causal Cauchy problem in a Gevrey class of index $\alpha=2$. The system becomes quasidiagonal hyperbolic if we posit a certain wave equation for the lapse function, and we can then relate the results to our previously obtained first order symmetric hyperbolic system for general relativity.

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