Gauge drivers for the generalized harmonic Einstein equations

Creators: Lindblom, Lee; Matthews, Keith D.; Rinne, Oliver; Scheel, Mark A.

Abstract

The generalized harmonic representation of Einstein's equations is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity community are incompatible with the hyperbolicity of the equations in this form. This paper presents a new method of imposing gauge conditions that preserves hyperbolicity for a much wider class of conditions, including as special cases many of the standard ones used in numerical relativity: e.g., K freezing, Gamma freezing, Bona-Massó slicing, conformal Gamma drivers, etc. Analytical and numerical results are presented which test the stability and the effectiveness of this new gauge-driver evolution system.

Additional Information

©2008 The American Physical Society. (Received 13 November 2007; published 1 April 2008) We thank Harald Pfeiffer and Bela Szilagyi for helpful comments concerning this work. 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 from the Sherman Fairchild Foundation and the Brinson Foundation, by NSF Grant Nos. DMS-0553302, PHY-0601459, PHY-0652995, and by NASA Grant No. NNG05GG52G.

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