On a Nonlinear Newtonian Gravity and Charging a Black Hole

Abstract

A scalar‑field gravitational analog of the Reissner‑Nordström solution is developed within a non‑linear Newtonian framework (also known as pseudo‑Newtonian gravity), where energy density of the field contributes to gravity. The model predicts an upper limit of charge that a central mass can accumulate, closely matching the general relativistic condition for black hole horizons. The dynamics of charging through isotropic proton bombardment are analyzed, showing that the Newtonian and general relativistic limits differ by a factor of four. The study isolates the effects of energy‑mass equivalence from spacetime curvature.