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arXiv · 1003.5122

Symplectic Integration of Post-Newtonian Equations of Motion with Spin

Christian Lubich·Benny Walther·Bernd Bruegmann
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Abstract

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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Christian Lubich, Benny Walther, Bernd Bruegmann. 2010-03-26. Symplectic Integration of Post-Newtonian Equations of Motion with Spin. https://doi.org/10.1103/physrevd.81.104025

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