Gravitational self-torque and spin precession in compact binaries

Abstract

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 $\ensuremath{\psi}$ per radian of orbital revolution for a particle carrying mass $\ensuremath{\mu}$ and spin $s\ensuremath{\ll}(G/c){\ensuremath{\mu}}^{2}$ in a circular orbit around a Schwarzschild black hole of mass $M\ensuremath{\gg}\ensuremath{\mu}$. We compute $\ensuremath{\psi}$ through $\mathcal{O}(\ensuremath{\mu}/M)$ in perturbation theory, i.e, including the correction $\ensuremath{\delta}\ensuremath{\psi}$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $\ensuremath{\delta}\ensuremath{\psi}$, 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.