Black hole solutions in functional extensions of Born-Infeld gravity

We consider electrovacuum black hole spacetimes in classical extensions of Eddington-inspired Born-Infeld gravity. By rewriting the Born-Infeld action as the square root of the determinant of a matrix (Omega) over tilde, we consider the family of models f (vertical bar(Omega) over tilde vertical bar) and study black hole solutions for a power-law family of models labeled by a simple parameter. We show how the innermost structure of the corresponding black holes is modified as compared to their general relativity counterparts, discussing in which cases a wormhole structure replaces the pointlike singularity. We go forward to argue that in such cases a geodesically complete and, thus, nonsingular spacetime is present, despite the existence of curvature divergences at the wormhole throat.