Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime

We generalize to Kerr spacetime previous gravitational self-force results on gyroscope precession along circular orbits in the Schwarzschild spacetime. In particular we present high order post-Newtonian expansions for the gauge invariant precession function along circular geodesics valid for an arbitrary Kerr spin parameter and show agreement between these results and those derived from the full post-Newtonian conservative dynamics. Finally we present strong field numerical data for a range of the Kerr spin parameter, showing agreement with the gravitational self-force-post-Newtonian results, and the expected lightring divergent behavior. These results provide useful testing benchmarks for self-force calculations in Kerr spacetime, and provide an avenue for translating self-force data into the spin-spin coupling in effective-one-body models.