**Authors**: Steven Detweiler

**Date**: 31 Aug 2009

**Abstract**: The gravitational field of a particle of small mass $\mu$ 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 $O(\mu)$. One part is an inhomogeneous field $hˆS_{ab}$ which, near the particle, looks like the Coulomb $\mu/r$ 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 $hˆR_{ab}$. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric $g_{ab}+hˆR_{ab}$. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

0908.4363
(/preprints)

2009-09-02, 11:20
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*