Identifying the singular field for self-force evaluation

Abstract

An introduction is given to the problem of self-force calculation for a point source. In elementary, electromagnetic, static examples it is obvious that the Coulomb field, which satisfies the inhomogeneous Maxwell equations, exerts no self-force. Relativistic motion and the curvature of spacetime make it more difficult to identify the singular field with comparable properties to the Coulomb field. A new Green's function has recently been found which aids in this identification, as a result of which the self-force can be shown to arise from a solution of the Maxwell equations which is homogeneous at the location of the point source. In the gravitational case, motion under the self-force is seen to be geodesic in a smoothly perturbed spacetime. The identity of the singular field which exerts no self-force is given, together with a rationale for the properties it possesses.