Hamiltonian Relaxation
arXiv:gr-qc/0501043 · doi:10.1088/0264-9381/22/12/009
Abstract
Due to the complexity of the required numerical codes, many of the new formulations for the evolution of the gravitational fields in numerical relativity are not tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars. This numerical setup is used to develop a new technique, the Hamiltonian relaxation (HR), that is benchmarked against the currently most stable simulations based on the BSSN method. We show that, while the length of the HR run is somewhat shorter than the equivalent BSSN simulation, the HR technique improves the overall quality of the simulation, not only regarding the satisfaction of the Hamiltonian constraint, but also the behavior of the total angular momentum of the binary. The latest quantity agrees well with post-Newtonian estimations for point-mass binaries in circular orbits.
More detailed description of the numerical implementation added and some typos corrected. Version accepted for publication in Class. and Quantum Gravity
References in corpus (17)
- Numerical simulation of orbiting black holes
- Numerical Relativity: A review
- Merger of binary neutron stars of unequal mass in full general relativity
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
- Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation
- Toward standard testbeds for numerical relativity
- A symmetry-breaking mechanism for the Z4 general-covariant evolution system
- Hydrodynamic Simulations in 3+1 General Relativity
- Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity
- Optimal Constraint Projection for Hyperbolic Evolution Systems
- Dynamical Determination of the Innermost Stable Circular Orbit of Binary Neutron Stars
- Controlling the Growth of Constraints in Hyperbolic Evolution Systems
- Relativistic Models for Binary Neutron Stars with Arbitrary Spins
- A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole
- Numerical stability of a new conformal-traceless 3+1 formulation of the Einstein equation
- The constraints as evolution equations for numerical relativity