Elementary development of the gravitational self-force

Abstract

The gravitational field of a particle of small mass m 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(m). One part is an inhomogeneous field h abS which, near the particle, looks like the Coulomb m â̂? 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 abR. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric g ab + h abR. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well. © 2011 Springer Science+Business Media B.V.