Generalized models for black-bounce solutions in $f(R)$ Gravity

TL;DR

This paper explores black-bounce solutions within $f(R)$ gravity, showing they can violate energy conditions less severely than in GR and proposing models with unique matter properties and horizons.

Contribution

It introduces generalized black-bounce solutions in $f(R)$ theories, analyzing energy condition violations and proposing models with novel matter configurations and horizons.

Findings

Energy condition violations are less severe than in GR.

Proposed a zero-density black-bounce model with horizons.

Developed models with positive energy density and $ ho+p_r>0$.

Abstract

In this article, the implementation of black-bounce solutions in $f(R)$ theories is investigated. Black-bounce solutions are regular configurations of the static spherically symmetric space-time, containing both black holes and wormholes structures. In General Relativity (GR), black-bounce solution implies violation of the energy conditions. We investigate the same issue in $f(R)$ theories using two strategies: first, supposing a given form for the $f(R)$ function and then determining the matter behavior; second, imposing a condition on the matter density and obtaining the resulting $f(R)$ function. In all cases, a given structure for the metric functions is supposed. Violation of the energy conditions still occur but they are less severe than in the corresponding GR cases. We propose a zero-density model that has horizons, which differs from the GR case. We also propose a model with positive energy density and show that $\rho+p_r>0$, which was not the case in GR.