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Implementation of higher-order absorbing boundary conditions for the Einstein equations

Rinne, Oliver and Buchman, Luisa T. and Scheel, Mark A. and Pfeiffer, Harald P. (2009) Implementation of higher-order absorbing boundary conditions for the Einstein equations. Classical and Quantum Gravity, 26 (7). 075009. ISSN 0264-9381.

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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 < ℓ, which include the widely used freezing-Ψ_0 boundary condition that imposes the vanishing of the Newman–Penrose scalar Ψ_0.

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Pfeiffer, Harald P.0000-0001-9288-519X
Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2009. Received 21 November 2008, in final form 30 January 2009. Published 10 March 2009. Print publication: Issue 7 (7 April 2009). We thank James Bardeen, Edvin Deadman, Lee Lindblom, Richard Matzner, Olivier Sarbach, Erik Schnetter, John Stewart and Manuel Tiglio for insightful suggestions and discussions during the course of this work and Keith Matthews for use of and help with his ODE integration code. The numerical simulations presented here were performed using the Spectral Einstein Code (SpEC) developed at Caltech and Cornell primarily by Larry Kidder, Harald Pfeiffer and Mark Scheel. This work was supported in part by grants to Caltech from the Sherman Fairchild Foundation and the Brinson Foundation, by NSF grants DMS-0553302, PHY-0601459, PHY-0652995 and by NASA grant NNG05GG52G. LTB was also supported by grants NSF PHY 03 54842 and NASA NNG 04GL37G to the University of Texas at Austin. OR gratefully acknowledges funding through a Research Fellowship at King’s College Cambridge.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
NSFPHY 03 54842
King’s College CambridgeUNSPECIFIED
Subject Keywords:PACS numbers: 04.25.D−, 02.60.Lj, 04.25.−g
Issue or Number:7
Record Number:CaltechAUTHORS:20090902-141024304
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Official Citation:Implementation of higher-order absorbing boundary conditions for the Einstein equations Oliver Rinne, Luisa T Buchman, Mark A Scheel and Harald P Pfeiffer 2009 Class. Quantum Grav. 26 075009 (24pp) doi: 10.1088/0264-9381/26/7/075009
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15554
Deposited By: George Porter
Deposited On:08 Sep 2009 16:10
Last Modified:09 Mar 2020 13:19

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