Revisiting the charged BTZ metric in nonlinear electrodynamics

In contrast to its chargeless version the charged Banados, Taitelboim and Zanelli (BTZ) metric in linear Maxwell electromagnetism is known to be singular at r=0. We show, by employing nonlinear electrodynamics that one obtains charged, extension of the BTZ metric with regular electric field. This we do by choosing a logarithmic Lagrangian for the nonlinear electrodynamics. A Theorem is proved on the existence of electric black holes and combining this results with a duality principle disproves the existence of magnetic black holes in 2+1-dimensions.