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arXiv · 0908.4363

Elementary development of the gravitational self-force

Steven Detweiler
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Abstract

The gravitational field of a particle of small mass $μ$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(μ)$. One part is an inhomogeneous field $h^S_{ab}$ which, near the particle, looks like the Coulomb $μ/r$ field with tidal distortion from the local Riemann tensor. This singular field is defined in a neighborhood of the small particle and does not depend upon boundary conditions or upon the behavior of the source in either the past or the future. The other part is a homogeneous field $h^R_{ab}$. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric $g_{ab}+h^R_{ab}$. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

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Steven Detweiler. 2009-08-31. Elementary development of the gravitational self-force. https://arxiv.org/abs/0908.4363

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