Three Dimensional Black Hole Coupled to the Born-Infeld Electrodynamics

TL;DR

This paper derives a new (2+1)-dimensional anti-de Sitter black hole solution coupled with Born-Infeld electrodynamics, revealing unique properties of the spacetime and electromagnetic field in a nonlinear regime.

Contribution

It presents the first derivation of a static circularly symmetric black hole solution with Born-Infeld electrodynamics in (2+1) dimensions, extending previous Maxwell-based models.

Findings

The solution is regular in metric and electric field at r=0.

Curvature invariants are singular at r=0, indicating a physical singularity.

The solution reduces to known Maxwell case in the weak field limit.

Abstract

A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained Einstein-Born-Infeld solution for certain range of the parameters (mass, charge, cosmological and Born-Infeld constants) represent a static circularly symmetric black hole. Although the covariant metric components and the electric field do not exhibit a singular behavior at r=0 the curvature invariants are singular at that point.