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 $\ddot{I}ˆ$ per radian of orbital revolution for a particle carrying mass $\hat{I}¼$ and spin $s\ll (G/c)\hat{I}{¼}^2$ in a circular orbit around a Schwarzschild black hole of mass $M\gg \hat{I}¼$. We compute $\ddot{I}ˆ$ through $O(\hat{I}¼/M)$ in perturbation theory, i.e, including the correction $\hat{I}´\ddot{I}ˆ$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $\hat{I}´\ddot{I}ˆ$, 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 semi-analytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.

5 pages, 1 table, 1 figure. Minor changes to match published version