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We derive the post-Newtonian dynamics for a spinning body with Corinaldesi-Papapetrou spin supplementary condition in Kerr spacetime. Both the equations of motion for the center of mass of the body and the spin evolution are obtained. For the non-relativistic case, our calculations show that the magnitude of spin measured in the rest frame of the body’s center of mass does not change with time, though the center of mass does not move along the geodesic. Moreover, we find that the effects of the spin-orbit and spin-spin couplings will be suppressed by the Lorentz factor when the body has a relativistic velocity.

Post-Newtonian dynamics basing on Mathisson-Papapetrou equations with Corinaldesi-Papapetrou condition in Kerr spacetime