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. 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 gyro-gravitomagnetic ratio $g_{S_{\ast }}(r,p_r,p_{\varphi })$ up to order $p_r^2\mathrm{/}{r}^4$ included.