Geometrical Well Posed Systems for the Einstein Equations

Y. Choquet-Bruhat; J. W. York,

Geometrical Well Posed Systems for the Einstein Equations

广义相对论与量子宇宙学 2012-08-27 v1

作者: Y. Choquet-Bruhat , J. W. York,

摘要

We show that, given an arbitrary shift, the lapse $N$ can be chosen so that the extrinsic curvature $K$ of the space slices with metric $\overline g$ in arbitrary coordinates of a solution of Einstein's equations satisfies a quasi-linear wave equation. We give a geometric first order symmetric hyperbolic system verified in vacuum by $\overline g$ , $K$ and $N$ . We show that one can also obtain a quasi-linear wave equation for $K$ by requiring $N$ to satisfy at each time an elliptic equation which fixes the value of the mean extrinsic curvature of the space slices.

关键词

general relativity static spherically symmetric solutions in general relativity partial differential equations

引用

@article{arxiv.gr-qc/9506071,
  title  = {Geometrical Well Posed Systems for the Einstein Equations},
  author = {Y. Choquet-Bruhat and J. W. York,},
  journal= {arXiv preprint arXiv:gr-qc/9506071},
  year   = {2012}
}

备注

13 pages, latex, no figures

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