Wormholes and nonsingular space-times in Palatini $f(R)$ gravity

TL;DR

This paper explores how Palatini $f(R)$ gravity coupled with Born-Infeld electrodynamics can produce nonsingular, wormhole-like space-times that replace traditional singularities, offering new insights into cosmic censorship.

Contribution

It demonstrates that in Palatini $f(R)$ gravity, charged black hole solutions can be nonsingular and feature wormhole structures, differing from classical solutions.

Findings

Singularities are replaced by finite-size wormholes.

Solutions match Reissner-Nordström at large distances.

Curvature divergences occur at the wormhole throat.

Abstract

We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric space-time, we find solutions which reduce to their Reissner-Nordstr\"om counterparts at large distances but undergo important non-perturbative modifications close to the center. Our new analysis reveals that the point-like singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular space-time, despite the existence of curvature divergences at the wormhole throat. Implications of these results, in particular for the cosmic censorship conjecture, are discussed.