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Orbital evolution of a test particle around a black hole: indirect determination of the self-force in the post-Newtonian approximation

Lior M Burko

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Comparing the corrections to Kepler's law with orbital evolution under a self-force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self-force in a post-Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self-force and spin–orbit coupling.


PACS

04.70.Bw Classical black holes

04.30.Db Wave generation and sources

04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations

MSC

83C25 Approximation procedures, weak fields

83C40 Gravitational energy and conservation laws; groups of motions

83C57 Black holes

83C10 Equations of motion

Subjects

Gravitation and cosmology

Dates

Issue 12 (21 June 2006)

Received 6 April 2006

Published 5 June 2006



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