(2+1)-Dimensional Black Hole with Coulomb-like Field

TL;DR

This paper derives a new (2+1)-dimensional black hole solution with a Coulomb-like electric field sourced by nonlinear electrodynamics, revealing unique properties of charged black holes in lower dimensions.

Contribution

It introduces a novel static black hole solution in (2+1) dimensions with a traceless energy-momentum tensor and Coulomb-like electric field, expanding understanding of lower-dimensional gravity models.

Findings

The electric field follows a Coulomb form, E(r)=q/r^2.

The solution describes both charged anti-de Sitter and flat spacetimes.

The spacetime is singular at the origin.

Abstract

A (2+1)-static black hole solution with a nonlinear electric field is derived. The source to the Einstein equations is a nonlinear electrodynamics, satisfying the weak energy conditions, and it is such that the energy momentum tensor is traceless. The obtained solution is singular at the origin of coordinates. The derived electric field E(r) is given by $E(r)=q/r^2$, thus it has the Coulomb form of a point charge in the Minkowski spacetime. This solution describes charged (anti)--de Sitter spaces. An interesting asymptotically flat solution arises for $\Lambda=0$.