Regular Power-Maxwell Black Holes

Abstract

We present a new class of regular, spherically symmetric spacetimes in nonlinear electrodynamics that are asymptotically dynamical but not de Sitter, exhibiting power-law Maxwell behavior at infinity. Generalizing to black holes, we derive their existence conditions and construct corresponding Penrose diagrams. Both the weak and dominant energy conditions are shown to be satisfiable. Magnetic solutions are first obtained, with electric counterparts derived via FP duality. Uniqueness conditions for the electric solutions are then established. Although electric duals are absent in square-root Maxwell theory, our auxiliary scalar formulation restores duality and enables a generalized duality transformation. The effective light propagation metric remains regular for particular magnetic configurations (without black holes) but becomes singular for electric cases. Additionally, spacelike photon trajectories are admitted in this spacetime. Finally, the ADM mass is shown to enter the Lagrangian, with the first law and Smarr formula derived, establishing the existence of thermodynamically stable black holes with positive heat capacity.