Born-Infeld gravity in three dimensions

In this paper we explore different aspects of three dimensional Born-Infeld as well as Born-Infeld-Chern-Simons gravity. We show that the models have anti–de Sitter and anti–de Sitter wave vacuum solutions. Moreover, we observe that although Born-Infeld-Chern-Simons gravity admits a logarithmic solution, Born-Infeld gravity does not, though it has a limiting logarithmic solution as we approach the critical point.