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

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.