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

Understand

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.