Generalized black-bounces solutions in f(R) gravity and their field sources

Abstract: In this work, following our recent findings in [1], we extend our analysis to explore the generalization of spherically symmetric and static black-bounce solutions, known from General Relativity, within the framework of the $f(R)$ theory in the metric formalism. We develop a general approach to determine the sources for any model where $f(R) = R + H(R)$, provided that the corresponding source for the bounce metric in General Relativity is known. As a result, we demonstrate that black-bounce solutions can emerge from this theory when considering the coupling of $f(R)$ gravity with nonlinear electrodynamics and a partially phantom scalar field. We also analyzed the energy conditions of these solutions and found that, unlike in General Relativity, it is possible to satisfy all energy conditions in certain regions of space-time.