Three dimensional black bounces in $f(R)$ gravity

TL;DR

This paper explores black bounce solutions in 2+1 dimensions within $f(R)$ gravity, analyzing their matter sources, constructing new solutions, and examining the viability and energy conditions of these models.

Contribution

It extends black bounce solutions to $f(R)$ gravity, introduces solutions with vanishing curvature scalar, and assesses matter support and energy conditions in these theories.

Findings

Black bounce solutions can be supported in $f(R)$ gravity with specific matter sources.

New solutions with zero curvature scalar are constructed within the framework.

Energy conditions are modified by $f(R)$ theories, affecting the exoticity of matter required.

Abstract

We investigate the existence of black bounce solutions in $2+1$ dimensions within the framework of $f(R)$ gravity. We analyze whether black bounce geometries originally obtained in general relativity can be consistently generalized to $f(R)$ theories and identify the matter sources capable of supporting such solutions. We also construct a new class of solutions by imposing a vanishing curvature scalar. In the matter sector, we consider models involving a coupling between a scalar field and nonlinear electrodynamics, while in the gravitational sector we analyze both the Starobinsky model and more general forms of $f(R)$. We further examine the viability conditions of the $f(R)$ models that give rise to these spacetimes, including the behavior of the scalaron mass. Finally, we study the associated energy conditions, in order to assess the degree of exoticity of the matter content required to sustain these black bounce solutions and how the $f(R)$ theory modifies the energy conditions.