标题： 广义模型在$f(R)$引力中的黑洞跳跃解 显示英文标题

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

摘要： 本文研究了在$f(R)$理论中黑蹦极解的实现。黑蹦极解是静态球对称时空的规则构型，包含黑洞和虫洞结构。在广义相对论（GR）中，黑蹦极解意味着能量条件的违反。我们使用两种策略在$f(R)$理论中研究相同的问题：首先，假设一个给定形式的$f(R)$函数，然后确定物质的行为；其次，对物质密度施加一个条件，并得到相应的$f(R)$函数。在所有情况下，假设了度规函数的一个特定结构。能量条件的违反仍然存在，但它们比相应的GR情况更为轻微。我们提出了一种具有视界的零密度模型，这与GR情况不同。我们还提出了一种具有正能量密度的模型，并展示了$\rho+p_r>0$，而这在GR中并非如此。 显示英文摘要

摘要： 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.