The Research Of Chaos In System Of Two Black Holes With Next-to-leading Order Spin Coupling

Compact binary systems are likely the most promising sources for futuregravitational wave detectors. It’s made of neutron stars and/or black holes, as a highnonlinear and non-integrable relativistic two-body problem, have richer dynamicphenomena of resonance and chaos. In recent years, with the more and more attentionon the detection of the gravitational wave, the research of compact binary systems hasalso become a hot spot. The main work in this paper is research the chaos in compactbinary with next-to-leading order spin-spin interactions.We take into account the dynamics of a complete third post-Newtonian (3PN)conservative Hamiltonian of two spinning black holes, where the orbital part arrivesat the third post-Newtonian precision level, the spin-orbit part up to next-to-leadingorder contributions and the spin-spin part accurate to the next-to-leading ordercontributions. It’s a12-dimensional system which have four independent isolatingintegrals, including the total energy, three components of the total angular momentumvector, so it’s non-integrable.On the one hand, It is shown through numerical simulations that thenext-to-leading order spin-spin couplings play an important role in chaos and thechaos becomes easier when the NLO spin-spin terms are included. This soundsreasonable, because the occurrence of chaos is completely due to the spin-spincouplings, which include particularly the NLO spin-spin contributions leading to asharp increase in the strength of nonlinearity. On the other hand, based on parametersscans of the higher-order spinning compact binary system we foud many chaoticorbits and some chaotic orbits whose initial radii are larger than10M and whoseLyapunov times are less than the corresponding inspiral decay times, that is to say,they become chaotic before coalescence.