Perspective on gravitational self-force analyses

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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 distortion caused by the spacetime. This singular part h is described in different coordinate systems and in different gauges. Subtracting h from hab leaves a regular remainder h. The self-force on the particle from its own gravitational field adjusts the world line at (μ) to be a geodesic of gab+h; 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 (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.