Testing complexity to diagnose wormholes existence: static and spherically symmetric case

Abstract In this paper, we examine static and spherically symmetric wormhole solutions in the context of Einstein–Cartan gravity, incorporating quantum corrections through the Casimir energy density as a matter source. To investigate the impact of quantum gravitational features, we apply the Generalized Uncertainty Principle (GUP), using the Dentournay, Gabriel, and Spindel (DGS) and Kempf, Mangano, and Mann (KMM) two GUP techniques. These GUP formalisms are implemented into the Casimir energy profile to investigate their effects on the wormhole geometry and matter content. We discuss the conservation equation, analyze the behavior of the null energy condition, and calculate the active gravitational mass to explore the physical acceptability of the wormhole solutions. In addition, we examine the complexity factor to describe the anisotropic character of the matter distribution filling the wormhole. The findings of this study demonstrate that GUP-induced corrections have a significant impact on the energy conditions, gravitational mass distribution, and structural complexity of the wormhole, indicating that Einstein–Cartan gravity, when incorporated with quantum vacuum effects, is capable of sustaining traversable wormhole geometries.