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We present the details of a model in general relativity of a small chargedblack hole moving in an external gravitational and electromagnetic field. Theimportance of our model lies in the fact that we can derive the equations ofmotion of the black hole from the Einstein-Maxwell vacuum field equationswithout encountering infinities. The key assumptions which we base our resultsupon are that (a) the black hole is isolated and (b) near the black hole thewave fronts of the radiation generated by its motion are smoothly deformedspheres. The equations of motion which emerge fit the pattern of the originalDeWitt and Brehme equations of motion (after they "renormalise"). Ourcalculations are carried out in a coordinate system in which the nullhypersurface histories of the wave fronts can be specified in a simple way,with the result that we obtain a new explicit form, particular to our model,for the well-known "tail term" in the equations of motion.

Equations of Motion in General Relativity of a Small Charged Black Hole