Dynamics of High-Order Spin-Orbit Couplings about Linear Momenta in Compact Binary Systems

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2017,（9）
• 页码范围: 375-381
• 页数: 7页
• 语种: 英文
• DOI: 10.1088/0253-6102/68/3/375

摘要

This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries,consisting of the Newtonian Kepler problem and the leading,next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta.When this Hamiltonian form is transformed to a Lagrangian form,besides the terms corresponding to the same order terms in the Hamiltonian,several additional terms,third post-Newtonian (3PN),4PN,5PN,6PN and 7PN order spin-spin coupling terms,yield in the Lagrangian.That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations.The full Lagrangian without the spin-spin couplings truncated is integrable and regular.Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped.These results are also supported numerically.