Nonsingular Black Holes in $f(R)$ Theories

TL;DR

This paper explores static, spherically symmetric solutions in a specific $f(R)$ gravity theory, revealing black hole models where the singularity is replaced by a finite-size wormhole, resulting in geodesically complete, nonsingular spacetimes.

Contribution

It introduces a class of $f(R)$ gravity solutions with wormhole structures replacing singularities, demonstrating geodesic completeness despite curvature divergences.

Findings

Black holes with wormhole cores replacing singularities.

Geodesic completeness despite curvature divergences.

Null geodesics take infinite affine time to reach the wormhole.

Abstract

We study the structure of a family of static, spherically symmetric space-times generated by an anisotropic fluid and governed by a particular type of $f(R)$ theory. We find that for a range of parameters with physical interest, such solutions represent black holes with the central singularity replaced by a finite size wormhole. We show that time-like geodesics and null geodesics with nonzero angular momentum never reach the wormhole throat due to an infinite potential barrier. For null radial geodesics, it takes an infinite affine time to reach the wormhole. This means that the resulting space-time is geodesically complete and, therefore, nonsingular despite the generic existence of curvature divergences at the wormhole throat.