Abstract
We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.
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Hogan, P.A., Robinson, I. The motion of charged test particles in general relativity. Found Phys 15, 617–627 (1985). https://doi.org/10.1007/BF01882486
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DOI: https://doi.org/10.1007/BF01882486