Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry

@article{Blanchet2009PostNewtonianAN,
  title={Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry},
  author={Luc Blanchet and Steven Lawrence Detweiler and Alexandre Le Tiec and Bernard F. Whiting},
  journal={Physical Review D},
  year={2009},
  volume={81},
  pages={064004}
}
The problem of a compact binary system whose components move on circular orbits is addressed using two different approximation techniques in general relativity. The post-Newtonian (PN) approximation involves an expansion in powers of v/c<<1, and is most appropriate for small orbital velocities v. The perturbative self-force analysis requires an extreme mass ratio m{sub 1}/m{sub 2}<<1 for the components of the binary. A particular coordinate-invariant observable is determined as a function of… 

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