The current paper is devoted to investigating wormhole solutions with an exponential gravity model in the background of $f\left(\mathcal{R}\right)$ theory. Spherically symmetric static spacetime geometry is chosen to explore wormhole solutions with anisotropic fluid source. The behavior of the traceless matter is studied by employing a particular equation of state to describe the important properties of the shape-function of the wormhole geometry. Furthermore, the energy conditions and stability analysis are done for two specific shape-functions. It is seen that the energy condition are to be violated for both of the shape-functions chosen here. It is concluded that our results are stable and realistic.

中文翻译：

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f（R）指数引力背景下的稳定虫洞

本文的研究背景是指数引力模型研究虫洞解。 $F（\mathcal{[R}）$ 理论。选择球面对称的静态时空几何来探索具有各向异性流体源的虫洞解决方案。通过采用特定的状态方程来描述虫孔几何形状函数的重要属性，研究了无痕迹物质的行为。此外，针对两个特定的形状函数进行了能量条件和稳定性分析。可以看出，此处选择的两个形状函数都违反了能量条件。结论是我们的结果是稳定和现实的。