Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry

A small mass mu in orbit about a much more massive black hole m moves along a world line that deviates from a geodesic of the black hole geometry by O(mu/m). This deviation is said to be caused by the gravitational self-force of the metric perturbation h(ab) from mu. For circular orbits about a nonrotating black hole we numerically calculate the O(mu/m) effects upon the orbital frequency and upon the rate of passage of proper time on the world line. These two effects are independent of the choice of gauge for h(ab) and are observable in principle. For distant orbits, our numerical results agree with a post-Newtonian analysis including terms of order (v/c)(6).