Second post-Newtonian Lagrangian dynamics of spinning compact binaries
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
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DOI：
10.1140/epjc/s10052-016-4339-7
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Li Huang;Xin Wu;D. Ma
中科院分区：
文献类型：
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作者：
Li Huang;Xin Wu;D. Ma
前序自旋-轨道耦合包含在自旋紧凑双星的后牛顿拉格朗日公式中，它由牛顿项、第一后牛顿项(1PN)和2PN非自旋项以及2PN自旋-自旋耦合组成。这导致在导出的哈密顿量中发生3PN自旋-自旋耦合。自旋-自旋耦合是哈密顿系统中混沌的主要原因。然而，与2PN自旋-自旋拉格朗日量等价的2PN自旋-自旋哈密顿量相比，3PN自旋-自旋哈密顿量很小，并且具有不同的符号。结果表明，在没有自旋-轨道耦合的拉格朗日方程中，发生混沌的几率比在有自旋-轨道耦合的拉格朗日方程中要大。数字证据支持这一说法。
The leading-order spin–orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin–spin coupling. This leads to a 3PN spin–spin coupling occurring in the derived Hamiltonian. The spin–spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin–spin Hamiltonian is small and has different signs, compared with the 2PN spin–spin Hamiltonian equivalent to the 2PN spin–spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin–orbit coupling is larger than that in the Lagrangian formulation with the spin–orbit coupling. Numerical evidences support this claim.