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

Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the effective Hamiltonian and the real one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Pade-resummed coefficients) which depends on the choice of some basic effective spin vector S-eff, and which is deformed by comparable-mass effects; and (iv) an additional effective spin-orbit interaction term involving another spin vector sigma. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter (a) over cap (LSO)equivalent to cJ(LSO)/(G(H-LSO/c(2))(2)). We find that the inclusion of NLO spin-orbit terms has a significant moderating effect on the dynamical characteristics of the circular orbits for large and parallel spins.