Exploring traversable wormholes in modified theory: Complexity and VIQ perspective under solitonic quantum wave dark matter halo

The traversable wormholes are analyzed in this study, incorporating the quantum wave dark matter halo and the electromagnetic field, in the framework of $f(R,T)$ gravity. The wormhole model is built upon the Morris-Thorne geometry, and the corresponding motion equations are derived for an anisotropic fluid within a typical modified gravity framework. Our next step is to derive the shape functions by considering distinct redshift parameters. These two functions adhere to the required conditions, linking two asymptotically flat regions of spacetime. We then proceed to formulate a couple of solutions through the resulting shape functions and make sure that they are in accordance with the violation of null energy bounds. Moreover, we assess the complexity factor and active gravitational mass, studying the point or area on the manifold where they approach to zero. It is demonstrated that both these quantities gain negative values in particular spacetime areas. The study also looks into the physical properties of wormholes, paying attention to the volume integral quantifier and embedding diagrams. The conclusions point to the fact that the derived wormhole geometries fulfill the necessary requirements, enabling them to exist within the modified gravity framework under consideration.