Title:         Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations

Authors:       Douglas N. Arnold and Nicolae Tarfulea

Source:        Electronic Journal on Differential Equations, Conf. 15 (2007), pp. 11-27

Status:        Published

Abstract:      Specifying boundary conditions continues to be a
challenge in numerical  relativity in order to obtain a long time
convergent numerical simulation of Einstein's equations in domains with
artificial boundaries. In this paper, we address this problem for the
Einstein--Christoffel (EC) symmetric hyperbolic formulation of
Einstein's equations linearized around flat spacetime. First, we
prescribe simple boundary conditions that make the problem well posed
and preserve the constraints. Next, we indicate boundary conditions for
a system that extends the linearized EC system by including the
momentum constraints and whose solution solves Einstein's equations in
a bounded domain. Finally, we extend our results to the case of
inhomogeneous boundary conditions.

Keywords:      general relativity, Einstein equations, boundary condition

Subj. class.:  35Q75, 35L50, 83C99

URL:           http://ima.umn.edu/~arnold/papers/ecbc.pdf