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

. 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

$$m-\frac{2}{3}q^{2}$$ m - 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 electromagnetic photon propagation using the effective optical geometry associated with the NED theory. The resulting photon-sphere condition differs from that obtained from null geodesics of the background metric. We find that the nonlinear optical corrections can produce appreciable deviations of the critical impact parameter from the Reissner–Nordström (RN) case, particularly in the strong-field regime. Our results highlight that nonlinear electrodynamics significantly enriches the causal structure, thermodynamic phase space, and electromagnetic propagation properties of charged black holes, leading to characteristic deviations from the RN paradigm.