Comment on "Linear superposition of regular black hole solutions of Einstein nonlinear electrodynamics"

TL;DR

This paper critiques and clarifies previous work on regular black hole solutions in Einstein nonlinear electrodynamics, emphasizing the importance of magnetic solutions and correcting inaccuracies regarding superpositions and Lagrangian properties.

Contribution

It provides corrections and clarifications to prior claims about regular black hole solutions, highlighting the role of magnetic solutions and the limitations of superpositions.

Findings

Magnetic solutions have features similar to electric ones but are often overlooked.

Regular solutions with electric charge cannot have a Maxwell weak-field limit.

Superpositions of regular solutions require careful consideration due to inaccuracies.

Abstract

It is argued that in the paper by A.A. Garcia-Diaz and G. Gutierrez-Cano [Phys. Rev. D 100, 064068 (2019)] on nonlinear electrodynamics coupled to general relativity, along with some interesting results and useful observations, many statements are either inaccurate or incomplete. In particular, the authors only consider solutions with an electric charge, whereas their magnetic counterparts have features of equal interest, both similar to and different from those of electric ones. Moreover, it is not mentioned that in electric solutions with a regular center the Lagrangian function $L(f)$ ($f = F_{\mu\nu} F^{\mu\nu}$) cannot have a Maxwell weak-field limit. The observation on superpositions of regular solutions suffers some inaccuracies. The present Comment tries to fill these and other gaps and to provide necessary corrections.