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

A small mass 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 (/m). This deviation is said to be caused by the gravitational self-force of the metric perturbation h₀₁ from. For circular orbits about a nonrotating black hole we numerically calculate the O (/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 h₀₁ and are observable in principle. For distant orbits, our numerical results agree with a post-Newtonian analysis including terms of order (v/c) ^6.