2010/03/26 by Christian Lubich, Benny Walther, Bernd Brügmann +1
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Numerical methods for differential equations #Pulsars and Gravitational Waves Research #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.81.104025
published as Phys.Rev.D81:104025,2010 · 9 pages, 6 figures
arxiv created 2010/03/26 · openalex publication_date 2010/05/12 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a noncanonically 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.