The non-existence of the self-accelerating dipole, and related questions

We calculate the self-force of a constantly accelerating electric dipole, showing, in particular, that classical electromagnetism does not predict that an electric dipole could self-accelerate, nor could it levitate in a gravitational field. We also resolve a paradox concerning the inertial mass of a longitudinally accelerating dipole, showing that the combined system of dipole plus field can be assigned a well-defined energy-momentum four-vector, so that the Principle of Relativity is satisfied. We then present some general features of electromagnetic phenomena in a gravitational field described by the Rindler metric, showing in particular that an observer fixed in a gravitational field described by the Rindler metric will find any charged object supported in the gravitational field to possess an electromagnetic self-force equal to that observed by an inertial observer relative to which the body undergoes rigid hyperbolic motion. It follows that the Principle of Equivalence is satisfied by these systems.