Abstract In this manuscript, the properties of topologically charged Morris–Thorne wormholes (WHs) are investigated within the framework of gravity, which modifies general relativity by introducing a generic function of Ricci scalar . The study primarily focuses on how different choices of shape functions influence the physical characteristics of WH models under consideration. To explore the viability of such WHs, the field equations in gravity are solved by considering an anisotropic energy‐momentum tensor (EMT). A key aspect of this investigation is the analysis of the matter content supporting these WHs, particularly whether it satisfies or violates the classical energy conditions, such as the Null, Weak, and Strong Energy Conditions. Unlike traditional WH solutions, which often require exotic matter with negative energy density, this study aims to examine the possibility of sustaining these structures with non‐exotic matter. Also, the influence of the global monopole charge are explored and the correction terms arising from modifications on the energy conditions, providing insights into their role in determining the physical plausibility of these WHs. The repulsive or attractive nature of the WHs is assessed by calculating the anisotropy parameter, which measures the deviation from isotropic pressure conditions. The results indicate that the global monopole parameter and the modifications introduced by gravity significantly affect the energy conditions, thereby controlling the physical viability of these WHs. This study contributes to a deeper understanding of traversable WHs in alternative gravity theories, potentially offering new avenues for theoretical and astrophysical research into exotic spacetime structures.
Asad et al. (Wed,) studied this question.