A new approach to equations of motion in general relativity is presented. Unlike the usual approaches, which rely on a regular background, this approach, by means of the method of spin coefficients, is based on the properties of the null cones emanating from a singular world line. We apply it to the Robinson-Trautman metrics as well as to their charged counterparts, and obtain exact equations of motion that give an intrinsic description of the behavior of a singularity in its own space-time. Two results of this approach are the discovery of an internal structure for a singularity and the surprising appearance of the Abraham radiation-reaction term in the charged case.

• Received 1 July 1969

DOI:https://doi.org/10.1103/PhysRev.187.1784