Free and constrained symplectic integrators for numerical general relativity
| dc.creator | Richter, Ronny | |
| dc.creator | Lubich, Christian | |
| dc.date | 2008-07-07 | |
| dc.date | 2008-11-04 | |
| dc.date.accessioned | 2026-07-07T11:52:16Z | |
| dc.date.available | 2026-07-07T11:52:16Z | |
| dc.description | We consider symplectic time integrators in numerical General Relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard symplectic integrator which here is explicit in the computationally expensive curvature terms. For the constrained evolution we give a formulation of the evolution equations that enforces the momentum constraints in a holonomically constrained Hamiltonian system and turns the Hamilton constraint function from a weak to a strong invariant of the system. This formulation permits the use of the constraint-preserving symplectic RATTLE integrator, a constrained version of the Stoermer-Verlet method. The behavior of the methods is illustrated on two effectively 1+1-dimensional versions of Einstein's equations, that allow to investigate a perturbed Minkowski problem and the Schwarzschild space-time. We compare symplectic and non-symplectic integrators for free evolution, showing very different numerical behavior for nearly-conserved quantities in the perturbed Minkowski problem. Further we compare free and constrained evolution, demonstrating in our examples that enforcing the momentum constraints can turn an unstable free evolution into a stable constrained evolution. This is demonstrated in the stabilization of a perturbed Minkowski problem with Dirac gauge, and in the suppression of the propagation of boundary instabilities into the interior of the domain in Schwarzschild space-time. | |
| dc.description | 25 pages, 7 figures; This version contains minor clarifications and corrections | |
| dc.identifier | https://arxiv.org/abs/0807.0734 | |
| dc.identifier | http://arxiv.org/abs/0807.0734 | |
| dc.identifier | Class.Quant.Grav.25:225018,2008 | |
| dc.identifier | doi:10.1088/0264-9381/25/22/225018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/204177 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Free and constrained symplectic integrators for numerical general relativity | |
| dc.type | text |