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

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

2006-11-02

arxiv.org/abs/gr-qc/0611010v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

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.

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