Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity

TL;DR

This paper derives exact, geodesically complete solutions in 2+1 dimensional Born-Infeld gravity coupled with an electric field, revealing nonsingular spacetimes with wormhole structures that extend the charged BTZ black hole solutions.

Contribution

It presents new analytical solutions in Born-Infeld gravity showing nonsingular, geodesically complete spacetimes with wormhole features, expanding understanding of metric-affine gravity models.

Findings

Two families of solutions are geodesically complete and nonsingular.

Solutions exhibit wormhole structures at their core.

Some solutions resemble charged BTZ black holes with richer horizon structures.

Abstract

We study Born-Infeld gravity coupled to a static, nonrotating electric field in $2+1$ dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of General Relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of General Relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom.