  We analytically compute the gravitational self-force correction to the
gyroscope precession along slightly eccentric equatorial orbits in the Kerr
spacetime, generalizing previous results for the Schwarzschild spacetime. Our
results are accurate through the 9.5 post-Newtonian order and to second order
in both eccentricity and rotation parameter. We also provide a post-Newtonian
check of our results based on the currently known Hamiltonian for spinning
binaries.

General Relativity and Quantum Cosmology