Perspective on gravitational self-force analyses

A point particle of mass μ moving on a geodesic creates a perturbation hab, of the spacetime metric gab, that diverges at the particle. Simple expressions are given for the singular μ/r part of hab and its tidal distortion caused by the spacetime. This singular part hab is described in different coordinate systems and in different gauges. Subtracting hab from hab leaves a regular remainder hab. The self-force on the particle from its own gravitational field adjusts the world line at O(μ) to be a geodesic of gab + h R ab; this adjustment includes all of the effects of radiation reaction. For the case that the particle is a small non-rotating black hole, we give a uniformly valid approximation to a solution of the Einstein equations, with a remainder of O(μ2) as μ→ 0. An example presents the actual steps involved in a self-force calculation. Gauge freedom introduces ambiguity in perturbation analysis. However, physically interesting problems avoid this ambiguity. PACS numbers: 04.25.-g, 04.20.-q, 04.70.Bw, 04.30.Db