Regular (2+1)-dimensional black holes within non-linear Electrodynamics

TL;DR

This paper derives a class of regular (2+1)-dimensional black hole solutions with nonlinear electrodynamics, ensuring regularity of the metric and invariants, and generalizes the method for various nonlinear Lagrangians.

Contribution

It introduces a new class of regular black hole solutions in (2+1) dimensions with nonlinear electrodynamics and provides a general solution derivation procedure.

Findings

Solutions are regular everywhere with finite curvature invariants.

The metric reduces to the (2+1)-BTZ solution in the weak field limit.

A general method for deriving solutions for any nonlinear electric Lagrangian is formulated.

Abstract

(2+1)-regular static black hole solutions with a nonlinear electric field are derived. The source to the Einstein equations is an energy momentum tensor of nonlinear electrodynamics, which satisfies the weak energy conditions and in the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class of solutions is regular; the metric, curvature invariants and electric field are regular everywhere. The metric becomes, for a vanishing parameter, the (2+1)-static charged BTZ solution. A general procedure to derive solutions for the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the electric field is formulated; for relevant electric fields one requires the fulfillment of the weak energy conditions.