Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-11-21
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav.
Scientific paper
10.1088/0264-9381/26/7/075009
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L
Buchman Luisa T.
Pfeiffer Harald P.
Rinne Oliver
Scheel Mark A.
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