2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215091Using the Teleparallel Equivalent of General Relativity formulated in Weitzenböck 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.8 pages, 1 figure. Accepted for publication in Phys. Rev. DGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext