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

TL;DR

This paper critiques a previous work on regular black holes in general relativity, emphasizing the importance of non-Maxwell behavior of the Lagrangian for electric solutions and highlighting issues of referencing and solution consistency.

Contribution

It clarifies the necessity of non-Maxwell Lagrangian behavior in electric regular black hole solutions and points out missing references and issues in the prior work.

Findings

Regular black hole solutions require non-Maxwell Lagrangian behavior at small f.

Electromagnetic fields become singular at surfaces where L(f) branches.

Previous work lacked proper references and overlooked key physics.

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.