Chaos in two black holes with next-to-leading order spin-spin interactions

We take into account the dynamics of a complete third post-Newtonian conservative Hamiltonian of two spinning black holes, where the orbital part arrives at the third post-Newtonian precision level and the spin-spin part with the spin-orbit part includes the leading-order and next-to-leading-order contributions. It is shown through numerical simulations that the next-to-leading order spin-spin couplings play an important role in chaos. A dynamical sensitivity to the variation of single parameter is also investigated. In particular, there are a number of \textit{observable} orbits whose initial radii are large enough and which become chaotic before coalescence.