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

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

2008-04-22

arxiv.org/abs/0804.3529v1

Phys.Rev.D77:124026,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 2 figures, 1 table

Scientific paper

10.1103/PhysRevD.77.124026

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 non-rotating 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 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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