Hamiltonian Relaxation

TL;DR

This paper introduces Hamiltonian relaxation as a new numerical technique for simulating binary neutron stars, improving the accuracy of gravitational field evolution and angular momentum behavior compared to traditional methods.

Contribution

The paper presents a novel Hamiltonian relaxation method and demonstrates its effectiveness in binary neutron star simulations as a benchmark for numerical relativity.

Findings

Hamiltonian relaxation improves constraint satisfaction.

HR yields better angular momentum behavior.

Simulation results align with post-Newtonian estimates.

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.