Abstract Recently, He and Ma introduced a generic method to generate static, circular symmetric regular black holes in 2+1-dimensional gravity minimally coupled to nonlinear electrodynamics (NED). In their formalism, they considered spacetimes filled with pure radial electric field and as examples four different cases were studied. In accordance with their method, in the weak field limit, the regular black holes are supposed to reduce to the charged BTZ black hole and the NED Lagrangian admits the Maxwell linear theory. Inspired from their paper, in this Letter we address a common feature of the NED Lagrangian which has not been noticed by the author. It will be shown that the NED Lagrangians are actually hybrid functions whose behaviors at weak and strong field regimes are different. This is in analogy with its 3+1-dimensional counterpart which has been pointed out long ago by Bronnikov.

中文翻译：

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2+1 维中的规则电黑洞爱因斯坦非线性电动力学

摘要 最近，He 和 Ma 介绍了一种在 2+1 维引力最小耦合非线性电动力学 (NED) 中生成静态、圆形对称规则黑洞的通用方法。在他们的形式主义中，他们考虑了充满纯径向电场的时空，并作为例子研究了四种不同的情况。按照他们的方法，在弱场极限下，规则的黑洞应该还原为带电的BTZ黑洞，NED拉格朗日量承认麦克斯韦线性理论。受他们论文的启发，在这封信中，我们讨论了 NED 拉格朗日函数的一个共同特征，该特征未被作者注意到。将证明 NED 拉格朗日函数实际上是混合函数，其在弱场和强场状态下的行为是不同的。