Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 11-27. 

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

Authors: Douglas N. Arnold (Univ. of Minnesota, Minneapolis, USA)
         Nicolae Tarfulea (Purdue Univ. Calumet, Hammond, IN, USA)
 
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.

Published February 28, 2007.
Math Subject Classifications: 35Q75, 35L50, 83C99.
Key Words: General relativity; Einstein equations; boundary conditions.