Regular electric black hole in 2+1-dimensions Einstein-nonlinear electrodynamics

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.