Derivation of gravitational self-force

Abstract

We analyze the issue of "particle motion" in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics corresponding to having a body (or black hole) that is "scaled down" to 0 size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric and obtain the leading order perturbative corrections, which include gravitational self-force, spin force, and geodesic deviation effects. The status of the MiSaTaQuWa equation is explained as a candidate "self-consistent perturbative equation" associated with our rigorous perturbative result. © 2011 Springer Science+Business Media B.V.