Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-02-06
Class.Quant.Grav.26:145017,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
This version clarifies some points concerning the interpretation of the results
Scientific paper
10.1088/0264-9381/26/14/145017
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.
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