Wormhole solutions obtained by Morris and Thorne (MT) in general relativity (GR) is investigated in a modified theory of gravity. In the gravitational action, we consider f(R, T) which is a function of the Ricci scalar (R) and the trace of the energy-momentum tensor (T). In the framework of a modified gravity described by \(f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }\), where \(\alpha \), \(\beta \) and \(\lambda \) are coupling constants, MT wormhole (WH) solutions with normal matter are obtained for a relevant shape function. We have considered two different values of \(\beta \) leading to two forms of f(R, T)-gravity. The energy conditions are probed at the throat and away from the throat of the WH. It is found that the coupling parameters, \(\alpha \) and \(\lambda \) in the gravitational action play an important role in deciding the matter composition in the wormholes. It is found that for a given \(\lambda \), WH exists in the presence of exotic matter at the throat when \(\alpha <0\). It is demonstrated here that WH exists even without exotic matter for \(\alpha >0\) in the modified gravity. Two different shape functions are considered to obtain WH solutions that are permitted with or without exotic matter. It is noted that in a modified f(R, T) gravity MT WH is permitted with normal matter which is not possible in GR. It is demonstrated that a class of WH solutions exist with anisotropic fluid for \(\lambda \ne -8\pi \). However, for flat asymptotic regions with anisotropic fluids WH solutions cannot be realized when \(\lambda =-8\pi \). All the energy conditions are found consistent with the hybrid shape function indicating existence of WH even with normal matter for \(\lambda \rightarrow 0\).

莫里斯和索恩 (MT) 在广义相对论 (GR) 中获得的虫洞解在改进的引力理论中进行了研究。在引力作用中，我们考虑f ( R ,  T )，它是 Ricci 标量 ( R ) 和能量-动量张量 ( T )的迹线的函数。在由\(f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }\)描述的修正引力的框架中，其中\(\alpha \) , \(\beta \)和\(\lambda \)是耦合常数，对于相关的形状函数，获得了具有正常物质的 MT 虫洞 (WH) 解。我们已经考虑了\(\beta \) 的两个不同值导致两种形式的f ( R ,  T )-重力。在喉部和远离 WH 的喉部探测能量条件。发现引力作用中的耦合参数\(\alpha\)和\(\lambda\)在决定虫洞中的物质组成方面起着重要作用。发现对于给定的\(\lambda \)，当\(\alpha <0\)时，WH 存在于喉咙处存在奇异物质的情况下。这里证明了对于\(\alpha >0\)即使没有外来物质 WH 也存在在修正重力中。考虑两种不同的形状函数来获得允许有或没有外来物质的 WH 解。需要注意的是，在修改后的f ( R ,  T ) 重力 MT WH 中，正常物质是允许的，这在 GR 中是不可能的。证明了对于\(\lambda \ne -8\pi \)存在一类具有各向异性流体的 WH 解。然而，对于具有各向异性流体的平坦渐近区域，当\(\lambda =-8\pi \)时无法实现 WH 解。发现所有能量条件都与指示 WH 存在的混合形状函数一致，即使对于\(\lambda \rightarrow 0\)也是正常物质。