The Equivalence Principle and gravitational and inertial mass relation of classical charged particle

Abstract

We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged particles, actually, is a subtle combination of an applied external force and the radiation reaction force. It suggests, as the Equivalence Principle is valid, that the gravitational mass of charged particle should be slight greater than its inertial mass. However, an interesting new feature emerges from the unexpected behavior of the gravitational and inertial mass relation at very strong gravitational field, just reachable at the early stage of the universe or, perhaps, near massive black holes, with a divergence that introduces a critical field value. It signs that the Equivalence Principle should not be valid near to this critical field, which certainly coincides where the quantum effects turns to be relevant.