$(2+1)$-dimensional regular black holes with nonlinear electrodynamics sources

TL;DR

This paper develops a general method to construct regular black holes in (2+1) dimensions using nonlinear electrodynamics, ensuring no singularities and correct weak field behavior, and studies their thermodynamics.

Contribution

It introduces a new approach for constructing regular black holes in (2+1) dimensions based on specific metric conditions and nonlinear electrodynamics.

Findings

Constructed four explicit regular black hole solutions.

Verified the first law of black hole thermodynamics for these solutions.

Analyzed thermodynamic properties of the regular black holes.

Abstract

On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of $(2+1)$-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct $(2+1)$-dimensional regular black holes. In this manner, we construct four $(2+1)$-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes and verify the first law of black hole thermodynamics.