Outer boundary conditions for Einstein's field equations in harmonic coordinates

Details Outer boundary conditions for Einstein's field equations in harmonic coordinates Outer boundary conditions for Einstein's field equations in harmonic coordinates

2007-07-18

arxiv.org/abs/0707.2797v2

Class.Quant.Grav.24:6349-6378,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Added more details on specifying initial data and the numerical calculation of reflection coefficients. 24 pages, 11 figures.

Scientific paper

10.1088/0264-9381/24/24/012

We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-Psi0 boundary condition and the hierarchy of absorbing boundary conditions introduced by Buchman and Sarbach. Using the recent technique developed by Kreiss and Winicour based on an appropriate reduction to a pseudo-differential first order system, we prove well posedness of the resulting initial-boundary value problem in the frozen coefficient approximation. In view of the theory of pseudo-differential operators it is expected that the full nonlinear problem is also well posed. Furthermore, we implement some of our boundary conditions numerically and study their effectiveness in a test problem consisting of a perturbed Schwarzschild black hole.

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