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Improved outer boundary conditions for Einstein's field equations

Luisa T. Buchman·Olivier C. A. Sarbach
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Abstract

In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a given angular momentum number L. In this article, we generalize B_2 so that it can be applied to fairly general foliations of spacetime by space-like hypersurfaces and general outer boundary shapes and further, we improve B_2 in two steps: (i) we give a local boundary condition C_2 which is perfectly absorbing including first order contributions in 2M/R of curvature corrections for quadrupolar waves (where M is the mass of the spacetime and R is a typical radius of the outer boundary) and which significantly reduces spurious reflections due to backscatter, and (ii) we give a non-local boundary condition D_2 which is exact when first order corrections in 2M/R for both curvature and backscatter are considered, for quadrupolar radiation.

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Luisa T. Buchman, Olivier C. A. Sarbach. 2007-04-30. Improved outer boundary conditions for Einstein's field equations. https://doi.org/10.1088/0264-9381%2F24%2F12%2Fs20

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