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

TL;DR

This paper explores the relationship between gravitational and inertial mass for classical charged particles, revealing that strong gravitational fields can challenge the validity of the strong Equivalence Principle.

Contribution

It demonstrates that the gravitational mass of charged particles slightly exceeds inertial mass and identifies critical gravitational field values where the strong Equivalence Principle breaks down.

Findings

Passive gravitational mass is slightly greater than inertial mass for charged particles.

Existence of critical gravitational field values for electrons and protons.

Strong gravitational fields can invalidate the strong Equivalence Principle.

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 slight 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 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 electron and proton, these critical field values are $g_{c}\simeq 4.8\times 10^{31}m/s^{2}$ and $g_{c}\simeq 8.8\times 10^{34}m/s^{2}$, respectively.