Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-08T23:47:37.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Gauge and constraint degrees of freedom:from analytical to numerical approximations in 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)
Get access

Abstract

The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. 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 a generalization, quasi-stationary gauge conditions are also discussed, including numerical experiments with the gauge-waves testbed. The complementary 3+1 approach is also considered, where constraints are related instead with energy and momentum first integrals and the gauge must be provided separately. The relationship between the two formalisms is discussed in a more general framework (Z4 formalism). Different strategies in black hole simulations follow when introducing singularity avoidance as a requirement. More flexible quasi-stationary gauge conditions are proposed in this context, which can be seen as generalizations of the 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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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