Abstract
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.
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