A model problem for the initialboundary value formulation of Einstein's field equations
Abstract
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In particular, they should be compatible with the constraints, yield a well posed initialboundary value formulation and incorporate some physically desirable properties like, for instance, minimizing reflections of gravitational radiation. Motivated by the problem in General Relativity, we analyze a model problem, consisting of a formulation of Maxwell's equations on a spatially compact region of spacetime with timelike boundaries. The form in which the equations are written is such that their structure is very similar to the EinsteinChristoffel symmetric hyperbolic formulations of Einstein's field equations. For this model problem, we specify a family of Sommerfeldtype constraintpreserving boundary conditions and show that the resulting initialboundary value formulations are well posed. We expect that these results can be generalized to the EinsteinChristoffel formulations of General Relativity, at least in the case of linearizations about a stationary background.
 Publication:

arXiv eprints
 Pub Date:
 September 2004
 arXiv:
 arXiv:grqc/0409027
 Bibcode:
 2004gr.qc.....9027R
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 25 pages