# Second post-Newtonian Lagrangian dynamics of spinning compact binaries

Research paper by Li Huang, Xin Wu; DaZhu Ma

Indexed on: 20 Sep '16Published on: 03 Sep '16Published in: The European Physical Journal C

#### Abstract

Abstract 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.AbstractThe 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.