Radiation reaction and the self-force for a point mass in general relativity

A point particle of mass mu moving on a geodesic creates a perturbation h(mu), of the spacetime metric g(0), that diverges at the particle. Simple expressions are given for the singular mu/r part of h(mu) and its quadrupole distortion caused by the spacetime. Subtracting these from h(mu) leaves a remainder h(R) that is C1. The self-force on the particle from its own gravitational field corrects the world line at O(mu) to be a geodesic of g(0)+h(R). For the case that the particle is a small nonrotating black hole, an approximate solution to the Einstein equations is given with error of O(mu(2)) as mu-->0.