Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations
Abstract
We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the ADM formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as non-trivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced ``constraint-preserving'' boundary conditions becomes apparent.
Keywords
Cite
@article{arxiv.gr-qc/0310064,
title = {Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations},
author = {Simonetta Frittelli and Roberto Gomez},
journal= {arXiv preprint arXiv:gr-qc/0310064},
year = {2009}
}
Comments
v1: 9 pages. v2: sign error corrected in eq.(8) and relevant discussion amended accordingly. v3: short section added, to appear in Phys Rev D. v4: typos corrected, published version