Point-source idealization in classical field theories. I. Electromagnetic radiation damping of a system of two perturbed Reissner-Nordstroem singularities in the slow-motion limit

This paper calculates the leading resistive accelerations acting on a system of two slightly deformed Reissner-Nordstroem singularities due to the emission of electromagnetic radiation, using matched asymptotic expansions. The unperturbed Reissner-Nordstroem solutions are assumed to have large charge-to-mass ratios q/m and to be separated by a distance large compared to both m and q2/m. The problem is of interest primarily because of Rosenblum's use of point singularities in his calculation of the mechanical work done in small-angle gravitational scattering. Classical derivations of the electromagnetic equations of motion for a charged source were faced with the choice between indeterminate equations and divergences in the stress-energy. The use of asymptotic expansions about Reissner-Nordstroem solutions makes renormalization arguments unnecessary. The following paper compares the mechanical energy loss obtained from the present matching calculation to that predicted by the Lorentz-Dirac equation; which was derived using a point-particle assumption