Hyperbolic formulations of General Relativity with Hamiltonian structure
arXiv:1002.4119 · doi:10.1103/PhysRevD.86.123017
Abstract
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools which are applicable to either the first order in time, second order in space or the fully second order form of the equations of motion. For toy models we find that the Hamiltonian structure can simplify the proof of symmetric hyperbolicity. In GR we use a special structure of the principal part to prove symmetric hyperbolicity of a formulation that includes gauge conditions which are very similar to the puncture gauge.
Our mathematica scripts are available at http://na.mathematik.uni-tuebingen.de/~richter/
References in corpus (10)
- Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
- How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
- Geometry and Regularity of Moving Punctures
- Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
- Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
- BSSN in Spherical Symmetry
- Comments on Bona-Masso type slicing conditions in long-term black hole evolutions
- Stability of the puncture method with a generalized BSSN formulation
- Free and constrained symplectic integrators for numerical general relativity
- Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration
Cited by in corpus (6)
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- An Introduction to Well-posedness and Free-evolution
- Hyperbolicity of Physical Theories with Application to General Relativity
- Lecture Notes: Numerical Relativity in higher dimensional spacetimes
- Well-balanced high order finite difference WENO schemes for a first-order Z4 formulation of the Einstein field equations
- Dual Foliation Formulations of General Relativity