Symplectic Integration of Post-Newtonian Equations of Motion with Spin

Details Symplectic Integration of Post-Newtonian Equations of Motion with Spin Symplectic Integration of Post-Newtonian Equations of Motion with Spin

2010-03-26

arxiv.org/abs/1003.5122v1

Phys.Rev.D81:104025,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 6 figures

Scientific paper

10.1103/PhysRevD.81.104025

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In the context of the splitting, it is possible to integrate the individual terms of the spin-orbit and spin-spin Hamiltonians analytically, exploiting the special structure of the underlying equations of motion. The outcome is a symplectic, time-reversible integrator, which can be raised to arbitrary order by composition. A fourth-order version is shown to give excellent behavior concerning error growth and conservation of energy and angular momentum in long-term simulations. Favorable properties of the integrator are retained in the presence of weak dissipative forces due to radiation damping in the full post-Newtonian equations.

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