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We show that the locally constant force necessary to get a stable hyperbolicmotion regime for classical charged point particles, actually, is a combinationof an applied external force and of the electromagnetic radiation reactionforce. It implies, as the strong Equivalence Principle is valid, that thepassive gravitational mass of a charged point particle should be slight greaterthan its inertial mass. An interesting new feature that emerges from theunexpected behavior of the gravitational and inertial mass relation, forclassical charged particles, at very strong gravitational field, is theexistence of a critical, particle dependent, gravitational field value thatsigns the validity domain of the strong Equivalence Principle. For electron andproton, 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.

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