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Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

Rinne, O. (2006) Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations. Classical and Quantum Gravity, 23 (22). pp. 6275-6300. ISSN 0264-9381.

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This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with a subluminal normal component) are analysed using the Fourier–Laplace technique. We show that the system is boundary stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well posed even if non-zero initial and source data are included.

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Additional Information:© 2006 IOP Publishing Limited Received 12 June 2006, in final form 6 September 2006; Published 6 October 2006; Print publication: Issue 22 (21 November 2006) I am particularly grateful to Olivier Sarbach for many valuable discussions and to Mark Scheel for help with the Caltech–Cornell Spectral Einstein Code, which he developed jointly with Larry Kidder and Harald Pfeiffer. I further thank Lee Lindblom for suggesting this project and for encouragement throughout the work, Alexander Alekseenko for helpful discussions, and all of them for careful reading of the manuscript. This work was supported in part by a grant from the Sherman Fairchild Foundation, by NSF grants PHY-0244906 and PHY-0601459 and by NASA grants NAG5-12834 and NNG05GG52G.
Issue or Number:22
Record Number:CaltechAUTHORS:RINcqg06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5499
Deposited By: Archive Administrator
Deposited On:20 Oct 2006
Last Modified:02 Oct 2019 23:23

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