Repulsive anisotropy and global monopoles as gatekeepers of traversable wormhole models with modified gravitational insights

Abstract The influence of three distinct shape functions on the physical properties of anisotropic wormholes (WHs) with a global monopole charge (GMC) is investigated in the background of minimally coupled modified gravity. The essential geometric criteria for traversability are assessed by confirming the throat condition and the flareout requirement. The GMC parameter’s effect on the WH throat and surrounding curvature is visualized through 2D and 3D embedding diagrams which reveal that larger monopole values yield wider throats and smoother spatial curvature. To examine the feasibility of such WH models, we solve the modified field equations and analyze the classical energy conditions with relativistic corrections. Our analysis shows that the anisotropy parameter remains positive in all three cases, indicating a repulsive geometry, while this anisotropic repulsion counteracts gravitational collapse and supports the throat’s stability. Additionally, the volume integral quantifier estimates the total exotic matter (EM), demonstrating that only negligible amounts are necessary to maintain traversable geometries due to modified gravitational insights.