Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration
arXiv:0902.1109 · doi:10.1088/0264-9381/26/14/145017
Abstract
We consider two strongly hyperbolic Hamiltonian formulations of general relativity and their numerical integration with a free and a partially constrained symplectic integrator. In those formulations we use hyperbolic drivers for the shift and in one case also for the densitized lapse. A system where the densitized lapse is an external field allows to enforce the momentum constraints in a holonomically constrained Hamiltonian system and to turn the Hamilton constraint function from a weak to a strong invariant. These schemes are tested in a perturbed Minkowski and the Schwarzschild space-time. In those examples we find advantages of the strongly hyperbolic formulations over the ADM system presented in [arXiv:0807.0734]. Furthermore we observe stabilizing effects of the partially constrained evolution in Schwarzschild space-time as long as the momentum constraints are enforced.
This version clarifies some points concerning the interpretation of the results
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- Hyperbolic formulations of General Relativity with Hamiltonian structure
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