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 ψ per radian of orbital revolution for a particle carrying mass μ and spin s≪(G/c)μ2 in a circular orbit around a Schwarzschild black hole of mass M≫μ. We compute ψ through O(μ/M) in perturbation theory, i.e, including the correction δψ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for δψ, 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.

• Received 2 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.064011