Resurvey of order and chaos in spinning compact binaries

Abstract

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.

16 pages, 7 figures

References in corpus (5)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Lyapunov indices with two nearby trajectories in a curved spacetime
• Relativistic chaos is coordinate invariant
• Revisit on "Ruling out chaos in compact binary systems"
• Chaos and Order in Models of Black Hole Pairs

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• Symplectic Integration of Post-Newtonian Equations of Motion with Spin
• Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
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• Chaos in two black holes with next-to-leading order spin-spin interactions
• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
• Energy-conserving integrator for conservative Hamiltonian systems with ten-dimensional phase space
• Spinning Particle in Gravitational Field of Black Hole Involving Global Monopole
• Leading-order gravitational time delay of massive particles by a moving Schwarzschild lens