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Sixth Mississippi State Conference on Differential Equations and Computational Simula-tions, Electronic Journal of Differential Equations, Conference 15 (2007), pp. 1127.
 

Summary: Sixth Mississippi State Conference on Differential Equations and Computational Simula-
tions, Electronic Journal of Differential Equations, Conference 15 (2007), pp. 1127.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
BOUNDARY CONDITIONS FOR THE EINSTEIN-CHRISTOFFEL
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 Einstein-Christoffel (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 Arnowitt-Deser-Misner or ADM decomposition, Einstein's equations split
into a set of evolution equations and a set of constraint equations (see Section 2),

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics