Existence of Traversable Wormholes admitting Exotic Fluid Content under Specific Density Profiles in Teleparallelism-based Theory

The main objective of this work is to explore the theoretical existence of traversable wormholes in Rastall teleparallel theory under the matter source described by solitonic quantum wave and Navarro-Frenk-White density profiles. We utilize the Morris-Thorne geometric setup to describe the wormhole geometry, from which the anisotropic field equations are obtained in terms of the torsion scalar. Under a constant redshift function, we derive the shape functions in connection with both dark matter models and examine their compliance with traversability conditions. Both the obtained functions satisfy the defined criteria, creating a topological bridge between asymptotically flat spacetimes. The existence of wormhole solutions is further investigated by measuring the extent to which they violate the null energy condition. We further investigate other geometric features, such as computation of the active gravitational mass, the volume integral quantifier, the embedding diagrams, and an evaluation of the anisotropy. The analysis confirms that both wormhole solutions are theoretically viable under the presence of exotic fluid within the considered teleparallel-based framework.