Regularized Conformal Electrodynamics: Novel C-metric in (2+1) Dimensions

Conformal electrodynamics is a particularly interesting example of power Maxwell non-linear electrodynamics, designed to possess conformal symmetry in all dimensions. In this paper, we propose a regularized version of Conformal electrodynamics, minimally regularizing the field of a point charge at the origin by breaking the conformal invariance of the theory with a dimensionfull "Born-Infeld-like" parameter. In four dimensions the new theory reduces to the recently studied Regularized Maxwell electrodynamics, distinguished by its "Maxwell-like" solutions for accelerated and slowly rotating black hole spacetimes. Focusing on three dimensions, we show that the new theory shares many of the properties of its four-dimensional cousin, including the existence of the charged C-metric solution (currently unknown in the Maxwell theory).