Black hole solutions in functional extensions of Born-Infeld gravity

TL;DR

This paper explores black hole solutions in extended Born-Infeld gravity models, revealing how their internal structure can differ from General Relativity, including the emergence of wormholes that lead to non-singular, geodesically complete spacetimes.

Contribution

It introduces a family of $f(|\hat{\Omega}|)$ gravity models and analyzes their black hole solutions, highlighting the replacement of singularities with wormhole structures.

Findings

Black hole interiors are modified by the models, often forming wormholes.

Wormholes can replace point-like singularities, leading to non-singular spacetimes.

Curvature divergences occur at the wormhole throat but do not imply singularities.

Abstract

We consider electrovacuum black hole spacetimes in classical extensions of Eddington-inspired Born-Infeld gravity. By rewriting Born-Infeld action as the square root of the determinant of a matrix $\hat{\Omega}$, we consider the family of models $f (|\hat{\Omega}|)$, and study black hole solutions for a power-law family of models labelled 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 point-like singularity. We go forward to argue that in such cases a geodesically complete and thus non-singular spacetime is present, despite the existence of curvature divergences at the wormhole throat.