Comment on “Construction of regular black holes in general relativity”
Abstract
We claim that the paper by Zhong-Ying Fan and Xiaobao Wang on nonlinear electrodynamics coupled to general relativity [Phys. Rev. D 94,124027 (2016)], although correct in general, in some respects repeats previously obtained results without giving proper references. There is also an important point missing in this paper, which is necessary for understanding the physics of the system: in solutions with an electric charge, a regular center requires a non-Maxwell behavior of Lagrangian function $L(f)$, $(f={F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}})$ 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.