Charged Black Holes From a Novel Nonlinear Electrodynamics Model Based on Electric Potential Regularization

Abstract

We propose a nonlinear electrodynamics (NED) model constructed by regularizing the electric scalar potential of a point charge rather than its electric field. The motivation for this potential-based construction is that an elementary closed-form electrostatic potential can be employed directly in atomic and other quantum-mechanical bound-state problems, whereas in several established NED models the point-charge potential is non-elementary and such applications generally require approximations or numerical treatments. Additionally, the resulting electrostatic configuration is nonsingular, has finite self-energy, and recovers Maxwell electrodynamics asymptotically. We derive the corresponding parametric NED model and energy–momentum tensor and show that the weak, null, and dominant energy conditions are satisfied, while the strong energy condition is violated. By minimally coupling the model to Einstein gravity, we obtain an exact static and spherically symmetric charged black-hole solution with a rich horizon structure, including simple, double, and triple horizons as well as naked singularities, depending on the mass and charge parameters. The geometry approaches Reissner–Nordström asymptotically but exhibits significant strong-field deviations. We further analyze null and timelike geodesics of the background metric and identify parameter regimes admitting exterior stable metric-null circular orbits and static equilibrium configurations (Dyson-like shells). Thus, the construction provides an analytically tractable potential-based NED framework that connects charged black-hole solutions with possible future applications to quantum bound-state systems.