Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription

In this work we present an analytical gravitational self-force calculation of the spin-orbit precession along an eccentric orbit around a Schwarzschild black hole, following closely the recent prescription of Akcay, Dempsey, and Dolan, giving results to six post-Newtonian orders expanded in small eccentricity through e(2). We then transcribe this quantity within the effective-one-body (EOB) formalism, thereby determining several new, linear-in-mass-ratio contributions in the post-Newtonian expansion of the spin-orbit couplings entering the EOB Hamiltonian. Namely, we determine the second gyrogravitomagnetic ratio g(S*) (r, p(r), p(phi)) up to order p(r)(2)/r(4) included.