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We study the electromagnetic and gravitational fields of the proton andelectron in terms of the Einstenian gravity via the introduction of anarbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at lengthscales of the order of the reduced Compton wavelength, corrections fromdifferent values of the $g$-factor are not negligible and discuss the presenceof general relativistic effects in highly ionized heavy atoms. On the otherhand, since at the Compton-wavelength scale the gravitational field becomesspin dominated rather than mass dominated, we also point out the necessity ofincluding angular momentum as a source of corrections to Newtonian gravity inthe quantum description of gravity at this scale.

The influence of the Lande $g$-factor in the classical general relativistic description of atomic and subatomic systems