Complexity factor induced traversable wormhole models: monopole signatures and the quest for stability

Abstract In this draft, we investigate constant redshift function Morris–Thorne-like traversable wormhole (WH) models which described as a relativistic static fluid distribution in Schwarzschild-type coordinates with a topological global monopole charge under the influence of D -dimensional Einstein gravity. In this scenario we consider three distinct shape functions, while matter sector is supported by anisotropic fluid configuration. We show some basic criteria for the viability of all three shape function models, the radial null energy condition is generally violated while tangential components are satisfied in the vicinity of the throat for appropriately chosen parameter values. We examine that the active gravitational mass becomes negative near the throat which indicates the existence of exotic matter (EM) and positive anisotropy parameter helps in maintaining the throat stability, while the adiabatic indices lie above the relativistic threshold supporting the stability of the WH configurations. We also employ the complexity factor as a diagnostic tool for anisotropy and density inhomogeneity which reveals that the WH geometries evolve toward minimal complexity at large radial distances. We analyze the influence of monopole parameter on the WH’s throat and curvature through 2 D and 3 D embedding diagrams, however, the total amount of EM is estimated by utilizing volume integral quantifier (VIQ) approach in our considered gravity theory.