Ronny Richter 2009 Class. Quantum Grav. 26 145017 doi:10.1088/0264-9381/26/14/145017
Ronny Richter
Show affiliationsWe 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 us 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 a Schwarzschild space-time. In those examples, we find advantages of the strongly hyperbolic formulations over the Arnowitt–Deser–Misner (ADM) system presented in [28]. Furthermore, we observe stabilizing effects of the partially constrained evolution in Schwarzschild spacetime as long as the momentum constraints are enforced.
04.20.Fy Canonical formalism, Lagrangians, and variational principles
02.60.Jh Numerical differentiation and integration
04.20.Gz Spacetime topology, causal structure, spinor structure
65P10 Hamiltonian systems including symplectic integrators
Issue 14 (21 July 2009)
Received 6 February 2009, in final form 27 May 2009
Published 3 July 2009
Ronny Richter 2009 Class. Quantum Grav. 26 145017
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