Physical properties of charged black holes from the nonlinear electrodynamics model based on electric potential regularization

Abstract

We investigate static, spherically symmetric black hole solutions arising from Einstein gravity minimally coupled to a nonlinear electrodynamics (NED) model constructed from a regularized electric potential of a point charge. The resulting spacetime is characterized by three parameters, namely, the ADM mass $% M $, the electric charge $Q$, and the nonlinear scale $r_{0}$. We show that, depending on the values of $M$ and $Q$, the solutions exhibit a rich causal structure comprising black holes with single, double, and triple horizons, as well as naked singular geometries. The nature of the central singularity is determined by the combination $m-\frac{2}{3}q^{2}$, allowing for both spacelike and timelike singularities. We perform a detailed thermodynamic analysis by deriving the Hawking temperature and heat capacity, revealing the existence of two critical charge parameters that govern the thermal behavior. Below a critical charge, the black holes are thermally unstable, whereas above it a stable phase emerges within a finite range of horizon radii bounded by Davies points. For sufficiently large charge, extremal configurations with vanishing temperature arise, further constraining the stability region. We also investigate observational signatures by analyzing null geodesics and black hole shadows, showing that nonlinear electrodynamics corrections lead to noticeable deviations from the Reissner-Nordstr\"{o}m geometry, including the possible absence of a photon sphere beyond a critical charge. Our results highlight that nonlinear electrodynamics significantly enriches the causal structure, thermodynamic phase space, and dynamical response of charged black holes, providing potentially observable deviations from the Reissner-Nordstr\"{o}m paradigm.