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 e2. 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 gS*(r,pr,p?) up to order pr2/r4 included.