Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity
arXiv:0710.4425 · doi:10.1051/eas:0830006
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.
arXiv commentTalk given at the Spanish Relativity Meeting, Tenerife, September 2007
References in corpus (9)
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- New Formalism for Numerical Relativity
- Toward standard testbeds for numerical relativity
- Accurate Evolution of Orbiting Binary Black Holes
- Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations
- Almost-stationary motions and gauge conditions in General Relativity
- Late Time Analysis for Maximal Slicing of Reissner-Nordström Puncture Evolutions