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

MPS-Authors
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Alic,  Daniela
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0710.4425v1.pdf
(Preprint), 156KB

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Citation

Bona, C., & Alic, D. (2008). Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity. In Spanish Relativity Meeting - Encuentros Relativistas Españoles ERE2007 Relativistic Astrophysics and Cosmology Tenerife, Spring 2008 (pp. 69-80).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-9D06-9
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.