Gravitational self-torque and spin precession in compact binaries

We calculate the effect of self-interaction on the ``geodetic'' spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle per radian of orbital revolution for a particle carrying mass and spin s (G/c) ^2 in a circular orbit around a Schwarzschild black hole of mass M. We compute through O (/M) in perturbation theory, i. e, including the correction (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semianalytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.