Elementary development of the gravitational self-force

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.

38 pages, 4 figures, Lecture given at the "School on Mass" (Orleans, France, June 2008), uses Springer's "svmult.cls"