Electric charge in hyperbolic motion: arcane geometrical aspects

We look at an electric charge in hyperbolic motion, and we describe some arcane geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material point particles are replaced by infinitesimal length elements along their worldlines. We show that the four-force obtained from our geometrical model is very closely related to the "electrostatic" four-force obtained from Fokker's time symmetric action.