Comment on "Construction of regular black holes in general relativity"

Abstract: It is claimed that the paper by Zhong-Ying Fan and Xiaobao Wang [Phys. Rev. D 94, 124027 (2016), arXiv: 1610.02636] on nonlinear electrodynamics coupled to general relativity, being correct in general, in some respects repeats previously obtained results without giving proper references. There is also an important point missing in this paper, but necessary for understanding the physics of the system: in solutions with an electric charge, a regular center requires a non-Maxwell behavior of the Lagrangian function $L(f),\ (f= F_{\mu\nu} F^{\mu\nu})$ at small $f$. Therefore, in all electric regular black hole solutions with a Reissner-Nordstr\"om asymptotic, the Lagrangian $L(f)$ is different in different parts of space, and the electromagnetic field behaves in a singular way at surfaces where $L(f)$ suffers branching.