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Energy norms and the stability of the Einstein evolution equations

Lindblom, Lee and Scheel, Mark A. (2002) Energy norms and the stability of the Einstein evolution equations. Physical Review D, 66 (8). Art. No. 084014. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:LINprd02

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Abstract

The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic formulations of the equations, an exact expression for the growth rate is derived using an energy norm. This expression agrees with the growth rate determined by numerical solution of the equations. An approximate method for estimating the growth rate is also derived. This estimate can be evaluated algebraically from the initial data, and is shown to exhibit qualitatively the same dependence as the numerically determined rate on the parameters that specify the formulation of the equations. This simple rate estimate therefore provides a useful tool for finding the most well-behaved forms of the evolution equations.


Item Type:Article
Additional Information:©2002 The American Physical Society. Received 12 June 2002; published 28 October 2002. We thank H. Friedrich, J. Isenberg, M. Keel, L. Kidder, L. Lehner, V. Moncrief, R. O’Shaughnessy, H. Pfeiffer, B. Szilagyi, S. Teukolsky, M. Tiglio and J. Winicour for helpful discussions concerning this work. We also thank L. Kidder, H. Pfeiffer, and S. Teukolsky for allowing us to use the Cornell code to test our growth rate estimates. Some computations were performed on the IA-32 Linux cluster at NCSA. This research was supported in part by NSF grant PHY-0099568 and NASA grant NAG5-10707.
Group:TAPIR
Subject Keywords:SYMMETRICAL HYPERBOLIC SYSTEM; BLACK-HOLE SPACETIMES; BRANS-DICKE THEORY; NUMERICAL RELATIVITY; GENERAL-RELATIVITY; ASHTEKAR FORMULATION; EXCISION; VARIABLES; COLLAPSE; GAUGE
Record Number:CaltechAUTHORS:LINprd02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LINprd02
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.66.084014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2197
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Mar 2006
Last Modified:26 Dec 2012 08:47

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