Abstract
In a recent article, we constructed a hierarchy 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 paper, we generalize 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 in two steps: (i) we give a local boundary condition 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 which is exact when first-order corrections in 2M/R for both curvature and backscatter are considered, for quadrupolar radiation.
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