Effective one-body Hamiltonian of two spinning black holes with next-to-next-to-leading order spin-orbit coupling

Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian spin-orbit Hamiltonian for spinning binaries [J. Hartung and J. Steinhoff, arXiv: 1104.3079.] we improve the effective-one-body description of the dynamics of two spinning black holes by including NNLO effects in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order spin-orbit Hamiltonian computed in [T. Damour, P. Jaranowski, and G. Schaefer, Phys. Rev. D 78, 024009 (2008).]. The present effective-one-body Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the next-to-leading order spin-orbit coupling.