Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 11-27.

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

Douglas N. Arnold, Nicolae Tarfulea

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.

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Douglas N. Arnold
Institute for Mathematics and its Applications,
University of Minnesota, Minneapolis, Minnesota 55455, USA
Nicolae Tarfulea
Department of Mathematics, Purdue University Calumet
Hammond, Indiana 46323, USA

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