Black Hole-Wormhole transition in (2+1) Einstein -- anti-de Sitter Gravity Coupled to Nonlinear Electrodynamics

TL;DR

This paper derives exact solutions in (2+1) gravity with nonlinear electrodynamics, revealing conditions under which these solutions describe black holes or traversable wormholes, and exploring their parameter space.

Contribution

It determines the electromagnetic field tensor form and finds a family of exact solutions in (2+1) gravity coupled to nonlinear electrodynamics, including black holes and wormholes.

Findings

Solutions characterized by five parameters including mass, angular momentum, and charges.

Certain parameter inequalities yield traversable wormholes.

Fine-tuning the cosmological constant produces extremal black holes.

Abstract

In this paper we present two results in $(2+1)$ gravity coupled to nonlinear electrodynamics. First it is determined the general form of the electromagnetic field tensor in $(2+1)$ gravity coupled to nonlinear electrodynamics in stationary cyclic spacetimes. Secondly, it is determined a family of exact solutions in $(2+1)$ gravity sourced by a nonlinear electromagnetic field. The solutions are characterized by five parameters: mass $M$, angular momentum $J$, cosmological constant $\Lambda$ and two electromagnetic charges, $q_{\alpha}$ and $q_{\beta}$. Remarkably, the solution can be interpreted as a traversable wormhole, provided the fulfillment of certain inequalities by the characteristic parameters; fine tunning of the cosmological constant leads to an extreme black hole, whereas by switching off one of the electromagnetic charges, we obtain the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole.