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

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.