Born-Infeld type extension of (non-)critical gravity

We consider the Born-Infeld-type extension of (non-)critical gravity which is higher curvature gravity on anti-de Sitter space with specific combinations of scalar curvature and Ricci tensor. This theory may also be viewed as a natural extension of three-dimensional Born-Infeld new massive gravity to arbitrary dimensions. We show that this extension is consistent with the holographic c-theorem and that scalar graviton modes are absent in this theory. After showing that ghost modes in the theory can be truncated consistently by appropriate boundary conditions, we argue that the theory is classically equivalent to Einstein gravity at the nonlinear level. Black hole solutions are discussed from the viewpoint of the full nonlinear classical equivalence between the theory and Einstein gravity. Holographic entanglement entropy in the theory is also briefly commented on.