Two-scale magnetically charged regular black holes from nonlinear electrodynamics and a T-duality-inspired zero-point length

Abstract

We construct a two-scale, static, spherically symmetric regular black hole in Einstein gravity sourced by magnetic nonlinear electrodynamics (NED). The zero-point length $\ell$ regularizes the mass and charge profiles, whereas $q$ is the asymptotic magnetic charge. The geometry approaches Reissner-Nordstr\"om at large radius, reduces to the neutral zero-point-length solution for $q=0$, and coincides geometrically with the Ay\'on-Beato-Garc\'ia solution for $\ell=|q|$. For $q\neq0$, inverse reconstruction gives a single-valued magnetic Lagrangian with Maxwell asymptotics and a finite strong-field limit. The center is regular and is de Sitter, locally Minkowski, or anti-de Sitter according to the sign of $2M\ell-q^2$; the weak energy condition holds globally if and only if $3M\ell\geq2q^2$. We derive the extremality curve, the exact heat capacity, and homogeneous horizon-variation and Smarr identities while retaining the Wald area entropy. We also prove that every charged black hole in this family has a nondegenerate extraordinary NED optical metric throughout the domain of outer communication. The associated capture shadow is selected by the global minimum of the optical impact-parameter function and generally differs from the background-geodesic shadow. Weak-field calculations yield the periapsis, bending, time-delay, and redshift corrections; in particular, $\ell$ first appears beyond the standard first-post-Newtonian parameters. Finally, for minimally coupled test radiation in a cold transparent plasma, we obtain exact parametric shadow relations for power-law density profiles and combine Hamiltonian ray tracing with a Novikov-Thorne disk model. A separate extraordinary NED-plasma continuation is displayed only as a phenomenological prescription because a material plasma breaks the conformal ambiguity of the vacuum characteristic metric.