$f(R)$ theory is a modification of Einstein general relativity which has many interesting results in cosmology and astrophysics. To derive black hole solution in this theory is difficult due to the fact that it is fourth order differential equations. In this study, we use the first reliable deviation from general relativity which is given by the quadratic form of $f(R)=R+\beta R^2$, where $\beta$ is a dimensional parameter. We calculate the energy conditions of the charged black holes and show that all of them are satisfied for the Taub-NUT spacetime. Finally, we study some thermodynamic quantities such as entropy, temperature, specific heat and Gibbs free energy. The calculations of heat capacity and free energy show that the charged Taub-NUT black hole have positive values which means that it has thermal stability.

中文翻译：

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$f(R)$ 引力中带电球对称 Taub-NUT 黑洞解

$f(R)$ 理论是对爱因斯坦广义相对论的修改，它在宇宙学和天体物理学中有许多有趣的结果。由于该理论是四阶微分方程，因此很难推导出该理论中的黑洞解。在这项研究中，我们使用了广义相对论的第一个可靠偏差，它由 $f(R)=R+\beta R^2$ 的二次形式给出，其中 $\beta$ 是一个维度参数。我们计算了带电黑洞的能量条件，并表明所有这些条件都满足 Taub-NUT 时空。最后，我们研究了一些热力学量，如熵、温度、比热和吉布斯自由能。热容量和自由能的计算表明，带电的 Taub-NUT 黑洞具有正值，这意味着它具有热稳定性。