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Solving Einstein's equations with dual coordinate frames

Scheel, Mark A. and Pfeiffer, Harald P. and Lindblom, Lee and Kidder, Lawrence E. and Rinne, Oliver and Teukolsky, Saul A. (2006) Solving Einstein's equations with dual coordinate frames. Physical Review D, 74 (10). Art. No. 104006. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:SCHEprd06

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Abstract

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original inertial coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating-coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.


Item Type:Article
Additional Information:©2006 The American Physical Society (Received 13 July 2006; published 2 November 2006) This work was supported in part by a grant from the Sherman Fairchild Foundation to Caltech and Cornell, by NSF Grants No. PHY-0099568, No. PHY-0244906, and No. PHY-0601459, and NASA Grants No. NAG5-12834, No. NNG05GG52G at Caltech, and by NSF Grants No. PHY-0312072, No. PHY-0354631, and NASA Grant No. NNG05GG51G at Cornell.
Group:TAPIR
Record Number:CaltechAUTHORS:SCHEprd06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SCHEprd06
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.74.104006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6385
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:06 Dec 2006
Last Modified:26 Dec 2012 09:20

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