Theoretical Viability of Traversable Wormholes without Exotic Fluid Content: A Family of Solutions under Various Equations of State

This study examines traversable, viable wormhole solutions in a torsion-based modified theory of gravity, characterizing geometries governed by the anisotropic charged fluid content. The field equations are derived using the Morris-Thorne metric for a chosen linear model. Through the application of multiple equations of state, four distinct shape functions are derived. Each function is verified by comparing it with the important acceptance standards. Furthermore, we conduct a thorough examination of the null energy conditions to identify if exotic matter is required to support the wormhole solutions or not. The active gravitational mass and the embedding geometry are also investigated. We find that the former quantity grows asymptotically at significant radial separations from the throat. Afterwards, some more fundamental elements are discussed such as the volume integral quantifier, an evaluation of the equilibrium, and how the anisotropy functions at the throat. Crucially, we verify that the resulting configurations of charged wormholes meet all existence requirements in this theoretical paradigm, obtaining validity without the need for exotic matter.