Spin-perturbed orbits near black holes

A compact stellar mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such deviations need to be included with sufficient precision into wave-form models for the upcoming space-based gravitational-wave detector LISA. I will present the formulation and solution of the Hamilton-Jacobi equation of a generic geodesic in Kerr space-time perturbed by the spin-curvature coupling, the leading order finite-size effect. In return, this solution allows to compute a number of observables such as the turning points of the orbits as well as the fundamental frequencies of motion. These results essentially solve the question of conservative finite-size effects in extreme mass ratio inspirals.