Radiation Reaction and the Self-Force for a Point Mass in General Relativity

A point particle of mass μ moving on a geodesic creates a perturbation h^μ, of the spacetime metric g⁰, that diverges at the particle. Simple expressions are given for the singular μ/r part of h^μ and its quadrupole distortion caused by the spacetime. Subtracting these from h^μ leaves a remainder hR that is C¹. The self-force on the particle from its own gravitational field corrects the world line at O(μ) to be a geodesic of g⁰+hR. 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(μ²) as μ→0.