Regular Power-Maxwell Black Holes

TL;DR

This paper introduces a new class of regular black hole solutions in nonlinear electrodynamics with power-law Maxwell behavior, analyzing their properties, dualities, and thermodynamics, including stability and mass relations.

Contribution

It constructs and characterizes regular black hole solutions with novel nonlinear electrodynamics features, including duality and thermodynamic properties.

Findings

Existence of regular black hole solutions satisfying energy conditions.

Thermodynamically stable black holes with positive heat capacity.

Restoration of duality via auxiliary scalar formulation.

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.