This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions.

中文翻译：

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具有物质耦合的扩展的遥平行引力理论中的可穿越虫洞

本研究探讨了重力中高斯分布和洛伦兹分布的球对称虫洞解。高斯和洛伦兹非对易几何的基本思想作为量子物理学中物理上可接受的实质概念出现。当讨论修正引力理论中的虫洞几何时，这种具有高斯分布和洛伦兹分布的非对易几何的想法变得更加引人注目。这里我们考虑一个线性模型重力来研究可穿越的虫洞。特别是，我们使用高斯和洛伦兹非对易分布讨论虫洞几何的可能情况，以获得它们的精确形状函数。通过结合所涉及的未知参数的特定值，我们讨论了这里探索的新虫洞几何形状的不同特性。值得注意的是，对于非交换几何的两种情况，所涉及的物质都违反了弱能量条件，而存在物理上可行的虫洞解决方案的可能性。通过分析平衡条件，发现得到的解是稳定的。此外，我们提供了高斯和洛伦兹非对易框架下虫洞结构的嵌入图。而且，