On the equivalence principle and gravitational and inertial mass relation of classical charged particles

Abstract

We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged point particles, actually, is a combination of an applied external force and of the electromagnetic radiation reaction force. It implies, as the strong equivalence principle is valid, that the passive gravitational mass of a charged point particle should be slightly greater than its inertial mass. An interesting new feature that emerges from the unexpected behavior of the gravitational and inertial mass relation, for classical charged particles, at a very strong gravitational field, is the existence of a critical, particle-dependent, gravitational field value that signs the validity domain of the strong equivalence principle. For electrons and protons, these critical field values are gc ≃ 4.8 × 1031m s−2 and gc ≃ 8.8 × 1034m s−2, respectively.