Komal RasoolSP19-RMT-020LHR TP 6476Dr. Rabia Saleem2026-03-122020https://repository.cuilahore.edu.pk/handle/123456789/2745The main focus of this thesis is to explore the phenomena of the traversable wormhole (TWH) solutions with non-commutative (NC) geometry using con formal symmetries in the framework of Rastall like teleparallel gravity (RTG). Togetthis, wederivethebackgroundfieldequationsforwormhole(WH)geom etry within RTG. We calculate the solution of the corresponding field equations using Gaussian and Lorentzian matter-energy distributions under conformal motion. Using both these distributions, we gain analytic WH solutions in terms of few special math functions such as gamma, exponential and hypergeometric functions. Further, we check the viability of weak, strong, and null energy conditions (ECs) for the considered fluid distribution at the WH throat and interpret them graphically. We are interested in finding the impact of an additional Rastall parameteronNCWHgeometriesascomparedtoteleparallelgravity. Moreover, weexplainthepossible constraints for the positivity of active gravitational mass in bothdistributions. We also explore the stability of gained WH solutions using the modified equilibrium condition in terms of four different forces in RTG. It is concluded that the constructed solutions are physically viable and stable.enDr. Rabia Saleemsp19traversable wormhole (TWH)non-commutative (NC)Department of MathematicsMathematicsThesis