Exploration of GUP-corrected Casimir wormholes in extended teleparallel gravity with matter coupling

In this manuscript, we investigate the properties of Casimir wormholes within the framework of extended teleparallel gravity, incorporating the Generalized Uncertainty Principle. Both the Casimir effect and the Generalized Uncertainty Principle (GUP) originate from the concept of a fundamental minimum length. Our analysis explores the geometric and physical traits of these wormholes, examining two distinct GUP constructions namely the Kempf, Mangano, and Mann (KMM) model and the Detournay, Gabriel, and Spindel (DGS) model and their corresponding equations of state. We find that the resulting wormhole solutions exhibit anisotropic effects and violate the null energy condition, implying the presence of exotic fluid. By employing volume integral techniques, we compute the quantity of exotic fluid, providing new insights into the nature of these wormholes. Our study sheds light on the implications of GUP-corrected Casimir wormholes for our understanding of gravity and the structure of spacetime.