Symplectic Integration of Post-Newtonian Equations of Motion with Spin

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.

9 pages, 6 figures

References in corpus (3)

• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Resurvey of order and chaos in spinning compact binaries
• Symplectic integrators for classical spin systems

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• Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity
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• Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map
• Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian
• Dissipated Correction Map Method with Trapezoidal Rule for the Simulations of Gravitational Waves from Spinning Compact Binary