Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration

Understand

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.