On Born-Infeld Gravity in Weitzenbock spacetime

TL;DR

This paper investigates a Born-Infeld gravity theory within Weitzenbock spacetime, deriving second order field equations and demonstrating its ability to produce regular black hole and cosmological solutions without singularities.

Contribution

It introduces a Born-Infeld gravity formulation in Weitzenbock spacetime with second order equations and provides explicit solutions for black holes and cosmology.

Findings

Extended BTZ black hole exists with positive cosmological constant

Cosmological model yields a singularity-free scale factor

The theory produces well-behaved solutions in specific scenarios

Abstract

Using the Teleparallel Equivalent of General Relativity formulated in Weitzenb\"{o}ck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended BTZ black hole, which results to exist even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor results to be well behaved, giving so a singularity-free solution.