Wormholes are considered to be hypothetical tunnels connecting two distant regions of the universe or two different universes. In general relativity (GR), the formation of traversable WH requires the consideration of exotic matter that violates energy conditions (ECs). If the wormhole geometry can be described in modified gravitational theories without introducing exotic matter, it will be significant for studying these theories. In the paper, we analyze some physical properties of static traversable WH within the framework of f(R, T) modified gravitational theory. Firstly, we explore the validity of the null, weak, dominant and strong energy conditions for wormhole matter for the considered \(f(R,T)=R+\alpha R^2+\lambda T\) model. Research shows that it is possible to obtain traversable WH geometry without bring in exotic matter that violates the null energy condition (NEC) in the f(R, T) theory. The violation of the dominant energy condition (DEC) in this model may be related to quantum fluctuations or indicates the existence of special matter that violates this EC within the wormhole. Moreover, it is found that in the \(f(R,T)=R+\alpha R^2+\lambda T\) model, relative to the GR, the introduction of the geometric term \(\alpha R^2\) has no remarkable impact on the wormhole matter components and their properties, while the appearance of the matter-geometry coupling term \(\lambda T\) can resolve the question that WH matter violates the null, weak and strong energy condition in GR. Additionally, we investigate dependency of the valid NEC on model parameters and quantify the matter components within the wormhole using the “volume integral quantifier”. Lastly, based on the modified Tolman–Oppenheimer–Volkov equation, we find that the traversable WH in this theory is stable. On the other hand, we use the classical reconstruction technique to derive wormhole solution in f(R, T) theory and discuss the corresponding ECs of matter. It is found that all four ECs (NEC, WEC, SEC and DEC) of matter in the traversable wormholes are valid in this reconstructed f(R, T) model, i.e we provide a wormhole solution without introducing the exotic matter and special matter in f(R, T) theory.

虫洞被认为是连接宇宙两个遥远区域或两个不同宇宙的假设隧道。在广义相对论（GR）中，可穿越的WH的形成需要考虑违反能量条件（EC）的外来物质。如果虫洞的几何结构能够在不引入外来物质的情况下用修正的引力理论来描述，那么对于研究这些理论将具有重要意义。在本文中，我们在f ( R ,  T ) 修正引力理论框架内分析了静态可穿越 WH 的一些物理性质。首先，我们探讨了所考虑的\(f(R,T)=R+\alpha R^2+\lambda T\)模型中虫洞物质的零、弱、主导和强能量条件的有效性。研究表明，无需引入违反f ( R ,  T ) 理论中的零能量条件 (NEC) 的外来物质，就可以获得可穿越的 WH 几何形状。该模型中对主导能量条件（DEC）的违反可能与量子涨落有关，或者表明虫洞内存在违反此 EC 的特殊物质。而且发现在\(f(R,T)=R+\alpha R^2+\lambda T\)模型中，相对于GR，引入了几何项\(\alpha R^2\ )对虫洞物质成分及其性质没有显着影响，而物质-几何耦合项\(\lambda T\)的出现可以解决WH物质违反GR中的零、弱和强能量条件的问题。此外，我们研究了有效 NEC 对模型参数的依赖性，并使用“体积积分量化器”量化虫洞内的物质成分。最后，基于修正的托尔曼-奥本海默-沃尔科夫方程，我们发现该理论中的可遍历WH是稳定的。另一方面，我们利用经典的重构技术推导了f ( R ,  T )理论中的虫洞解并讨论了相应的物质EC。结果发现，可穿越虫洞中物质的所有四个EC（NEC，WEC，SEC和DEC）在这个重建的f（R，  T）模型中都是有效的，即我们提供了一个虫洞解，而没有引入奇异物质和特殊物质f ( R ,  T )理论。