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Gauge and constraint degrees of freedom:from analytical to numerical approximationsin General Relativity

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
C. Bona  and
D. Alic
C. Bona
Affiliation:
Departament de Fisica, Universitat de les Illes Balears, Institute for Applied Computation with Community Code (IAC3)
D. Alic
Affiliation:
Departament de Fisica, Universitat de les Illes Balears, Institute for Applied Computation with Community Code (IAC3)
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Abstract

The harmonic formulation of Einstein's field equations isconsidered, where the gauge conditions are introduced as dynamicalconstraints. The difference between the fully constrained approach(used in analytical approximations) and the free evolution one(used in most numerical approximations) is pointed out. As ageneralization, quasi-stationary gauge conditions are alsodiscussed, including numerical experiments with the gauge-wavestestbed. The complementary 3+1 approach is also considered, whereconstraints are related instead with energy and momentum firstintegrals and the gauge must be provided separately. Therelationship between the two formalisms is discussed in a moregeneral framework (Z4 formalism). Different strategies in blackhole simulations follow when introducing singularity avoidance asa requirement. More flexible quasi-stationary gauge conditions areproposed in this context, which can be seen as generalizations ofthe current “freezing shift” prescriptions.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 69 - 79
Copyright
© EAS, EDP Sciences, 2008

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References

Alcubierre, M., et al., 2004, Class. Quantum Grav., 21, 589613 CrossRef
Alic, D., Bona, C., Bona-Casas, C., & Massó, J., 2007, Phys. Rev. D, in press [arXiv:0706.1189]
Baker, J.G., et al., 2006, Phys. Rev. Lett., 96, 111102 CrossRef
Bernstein, D., 1993, Ph.D. Thesis (Dept. of Physics, Univ. of Illinois at Urbana-Champaign)
Bona, C., & Massó, J., 1988, Phys. Rev. D, 38, 2419 CrossRef
Bona, C., Massó, J., Seidel, E., & Stela, J., 1995, Phys. Rev. Lett., 75, 600 CrossRef
Bona, C., Ledvinka, T., Palenzuela, C., & Žáček, M., 2003, Phys. Rev., D, 67, 104005
Bona, C., Carot, J., & Palenzuela-Luque, C., 2005, Phys. Rev. D, 72, 124010 CrossRef
Bona, C., Lehner, L., & Palenzuela-Luque, C., 2005, Phys. Rev. D, 72, 104009 CrossRef
Campanelli, M., Lousto, C.O., Marronetti, P., & Zlochower, Y., 2006, Phys. Rev. Lett., 96, 111101 CrossRef
Fourés-Bruhat, Y., 1952, Acta Math., 88, 141 CrossRef
Choquet-Bruhat, Y., 1956, J. Rat. Mec. Analysis, 5, 951
Choquet-Bruhat, Y., 1967, in Gravitation: An Introduction to Current Research, ed. L. Witten (John Wiley, New York)
De Donder, T., 1921, La Gravifique Einstenienne (Gauthier-Villars, Paris)
De Donder, T., 1927, The Mathematical Theory of Relativity, Massachusetts Institute of Technology (Cambridge, MA)
Diener, P., et al., 2006, Phys. Rev. Lett., 96, 121101 CrossRef
Gustafson, B., Kreiss, H.O., & Oliger, J., 1995, Time dependent problems and difference methods (New York: Wiley)
Lichnerowicz, A., 1944, J. Math. Pures Appl., 23, 37
Pretorius, F., 2005, Phys. Rev. Lett., 95, 121101 CrossRef
Reimann, B., & Brügmann, B., 2004, Phys. Rev., D69 044006