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

TL;DR

This paper investigates how the Lande g-factor influences electromagnetic and gravitational fields of fundamental particles within a general relativistic framework, highlighting significant effects at quantum length scales and the importance of angular momentum in quantum gravity corrections.

Contribution

It introduces the role of the Lande g-factor in Kerr-Newman solutions to explore relativistic effects at quantum scales, emphasizing the significance of angular momentum in quantum gravity corrections.

Findings

g-factor variations affect fields at the Compton wavelength scale

Relativistic effects are significant in highly ionized heavy atoms

Angular momentum becomes a dominant source in quantum gravity corrections

Abstract

We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity via the introduction of an arbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the $g$-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.