 
Summary: Sixth Mississippi State Conference on Differential Equations and Computational Simula
tions, Electronic Journal of Differential Equations, Conference 15 (2007), pp. 1127.
ISSN: 10726691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
BOUNDARY CONDITIONS FOR THE EINSTEINCHRISTOFFEL
FORMULATION OF EINSTEIN'S EQUATIONS
DOUGLAS N. ARNOLD, NICOLAE TARFULEA
Abstract. Specifying boundary conditions continues to be a challenge in nu
merical relativity in order to obtain a long time convergent numerical sim
ulation of Einstein's equations in domains with artificial boundaries. In this
paper, we address this problem for the EinsteinChristoffel (EC) symmetric hy
perbolic 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 momen
tum constraints and whose solution solves Einstein's equations in a bounded
domain.
1. Introduction
In the ArnowittDeserMisner or ADM decomposition, Einstein's equations split
into a set of evolution equations and a set of constraint equations (see Section 2),
