Weak Interaction and Generalized Relativistic Acceleration Formulae

This paper presents a generalized formula for the acceleration of a body endowed with mass and electric charge, revealing possible new insights into the physics of ultra-dense objects like black holes and neutron stars. Traditionally, the Schwarzschild metric accounts for gravitational acceleration alone, whereas the Reissner-Nordström metric extends this picture by incorporating electric charge. In our approach, we derive the acceleration for a charged, spherical object directly from the geodesic equations and uncover a two-part structure: the familiar gravitational term and an additional repulsive term that we associate with the weak interaction. We verify this two-component model in the limiting case of a static electron, where its classical radius emerges naturally and aligns with laboratory measurements. More broadly, our findings highlight three potentially groundbreaking conclusions. First, by including a weak-interaction term, we extend Newton’s second law of motion to encompass relativistic effects of charged matter. Second, we demonstrate that the gravitational constant G may not represent gravity alone, but also subtle weak-interaction contributions - offering a novel explanation for longstanding challenges in measuring G. Finally, our analysis suggests that black-hole singularities can vanish if even a minimal net charge is present, sidestepping the infinite-density collapse predicted by the Schwarzschild solution. These results may spark further exploration into unifying gravitational and quantum regimes, particularly in the vicinity of ultra-dense astrophysical environments.