Perspective on gravitational self-force analyses

A point particle of mass μ 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 μ/ r part of h ab and its tidal distortion caused by the spacetime. This singular part h S ab is described in different coordinate systems and in different gauges. Subtracting h S ab from h ab leaves a regular remainder h R ab . The self-force on the particle from its own gravitational field adjusts the worldline at O(μ) to be a geodesic of g ab + 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(μ 2 ) 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.