Perspective on gravitational self-force analyses

A point particle of mass mu moving on a geodesic creates a perturbation h(ab), of the spacetime metric g(ab), that diverges at the particle. Simple expressions are given for the singular mu/r part of hab and its tidal distortion caused by the spacetime. This singular part h(ab)(S) is described in different coordinate systems and in different gauges. Subtracting h(ab)(S) from hab leaves a regular remainder h R. The self-force on the particle from its own gravitational field adjusts the worldline at O(mu) to be a geodesic of g(ab) + h(ab)(R); 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(mu(2)) as mu -> 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.