# 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…

## 65 Citations

### High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

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Recent numerical and analytic computations based on the self-force (SF) formalism in general relativity showed that half-integral post-Newtonian (PN) terms, i.e. terms involving odd powers of 1/c,…

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We present an analytic computation of Detweiler's redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no…

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The mass-type quadrupole moment of inspiralling compact binaries (without spins) is computed at the fourth post-Newtonian (4PN) approximation of general relativity. The multipole moments are defined…

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