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Using a recent, novel Hamiltonian formulation of the gravitationalinteraction of spinning binaries, we extend the Effective One Body (EOB)description of the dynamics of two spinning black holes to next-to-leadingorder (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonianis constructed from four main ingredients: (i) a transformation between the``effective'' Hamiltonian and the ``real'' one, (ii) a generalized effectiveHamilton-Jacobi equation involving higher powers of the momenta, (iii) aKerr-type effective metric (with Pad\'e-resummed coefficients) which depends onthe choice of some basic ``effective spin vector'' $\bf{S}_{\rm eff}$, andwhich is deformed by comparable-mass effects, and (iv) an additional effectivespin-orbit interaction term involving another spin vector $\bsigma$. As a firstapplication of the new, NLO spin-dependent EOB Hamiltonian, we compute thebinding energy of circular orbits (for parallel spins) as a function of theorbital frequency, and of the spin parameters. We also study thecharacteristics of the last stable circular orbit: binding energy, orbitalfrequency, and the corresponding dimensionless spin parameter $\hat{a}_{\rmLSO}\equiv c J_{\rm LSO}/\boldsymbol(G(H_{\rm LSO}/c^2)^2\boldsymbol)$. We findthat the inclusion of NLO spin-orbit terms has a significant ``moderating''effect on the dynamical characteristics of the circular orbits for large andparallel spins.

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