In this work, the possible existence of wormhole solutions have been investigated in the extended teleparallel [Formula: see text] theory of gravity by incorporating the Lorentzian source of non-commutative geometry through the conformal motion. The physical concept of conformal symmetry becomes more arguable when it is discussed in the background of non-commutative geometry, especially with the Lorentzian source. In this context, two specific different models of the extended teleparallel theory, that is, [Formula: see text], and [Formula: see text] (where [Formula: see text], [Formula: see text], [Formula: see text] being real constants and [Formula: see text] a positive integer) have been studied. The corresponding energy conditions are worked out and are analyzed graphically in the presence of the conformal motion with Lorentzian source. The presence of the exotic matter has been confirmed due to the violation of null energy conditions under some particular conditions, thereby proving the existence of the wormhole geometries in both of the models under investigation. Moreover, the stability of the wormhole geometries via the Tolman-Oppenheimer-Volkov equation has been discussed. It is concluded that these wormhole solutions supported by the non-exotic matter truly exist and are well stable under the extended teleparallel gravity.

中文翻译：

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在保角运动下具有非对角四分体的 f(T) 重力下的洛伦兹分布虫洞解

在这项工作中，通过将洛伦兹源通过共形运动结合非交换几何的洛伦兹源，在扩展的远程平行[公式：见文本]引力理论中研究了虫洞解的可能存在。当在非交换几何的背景下讨论共形对称的物理概念时，它变得更有争议，尤其是在洛伦兹源的情况下。在这种情况下，扩展的遥平行理论有两种具体的不同模型，即[公式：见文]和[公式：见文]（其中[公式：见文]，[公式：见文]，[公式：见文]见文本]是实常数和[公式：见文本]正整数）已被研究。计算出相应的能量条件，并在存在洛伦兹源的共形运动的情况下进行图形分析。由于在某些特定条件下违反了零能量条件，已经证实了外来物质的存在，从而证明了两个正在研究的模型中都存在虫洞几何形状。此外，通过 Tolman-Oppenheimer-Volkov 方程讨论了虫洞几何形状的稳定性。得出的结论是，这些由非奇异物质支持的虫洞解是真实存在的，并且在延伸的远平行重力下非常稳定。