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Outer boundary conditions for Einstein's field equations in harmonic coordinates

Ruiz, Milton and Rinne, Oliver and Sarbach, Olivier (2007) Outer boundary conditions for Einstein's field equations in harmonic coordinates. Classical and Quantum Gravity, 24 (24). pp. 6349-6377. ISSN 0264-9381. doi:10.1088/0264-9381/24/24/012.

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We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions, which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-Ψ0 boundary condition and the hierarchy of absorbing boundary conditions introduced by Buchman and Sarbach. Using the recent technique developed by Kreiss and Winicour based on an appropriate reduction to a pseudo-differential first-order system, we prove well posedness of the resulting initial-boundary value problem in the frozen coefficient approximation. In view of the theory of pseudo-differential operators, it is expected that the full nonlinear problem is also well posed. Furthermore, we implement some of our boundary conditions numerically and study their effectiveness in a test problem consisting of a perturbed Schwarzschild black hole.

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Additional Information:© 2007 IOP Publishing Ltd. Received 20 July 2007, in final form 26 October 2007. Published 29 November 2007. Print publication: Issue 24 (21 December 2007) It is a pleasure to thank J Bardeen, L Buchman, L Lindblom, O Reula, M Scheel and J Winicour for useful comments and discussions. The numerical simulations presented here were performed using the Spectral Einstein Code (SpEC) developed at Caltech and Cornell primarily by Larry Kidder, Mark Scheel and Harald Pfeiffer. This work was supported in part by Dirección General de Estudios de Posgrado (DEGP), by CONACyT through grants 47201-F and CONACYT 47209-F, by DGAPA-UNAM through grants IN113907, by grants CIC 4.20 to Universidad Michoacana, and by grants to Caltech from the Sherman Fairchild Foundation, NSF grant PHY-0601459 and NASA grant NNG05GG52G. M Ruiz thanks Universidad Michoacana de San Nicolás de Hidalgo for hospitality.
Issue or Number:24
Record Number:CaltechAUTHORS:RUIcqg07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9245
Deposited By: Archive Administrator
Deposited On:29 Nov 2007
Last Modified:08 Nov 2021 20:57

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