A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry

A small mass μin 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(μ/M). This deviation is said to be caused by the gravitational self-force of the metric perturbation h_{ab} from μ. For circular orbits about a non-rotating black hole we numerically calculate the O(μ/M) effects upon the orbital frequency and upon the rate of passage of proper time on the worldline. 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.

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