Probing wormholes supported by Casimir energy in noncommutative and GUP-corrected spacetimes

Abstract

We explore the effects of noncommutativity and generalized uncertainty principles (GUP) on the Casimir wormhole spacetime. Building on the work of Jusufi (Eur. Phys. J. C 80:127, 2020), we examine three specific GUP models: the Kempf, Mangano, and Mann (KMM) model; the Detournay, Gabriel, and Spindel (DGS) model; and the Type II model. Our study focuses on how corrections to the Casimir energy density, influenced by the presence of a minimal length \(x_0 = \hbar \sqrt{\theta }\), impact wormhole dynamics. We compare results from these models to the ones based on the noncommutative coherent state approach at higher orders of perturbation in \(\sqrt{\theta }\). Specifically, we derive expressions for the shape function, light deflection angle in the weak deflection limit, ADM mass of the wormhole, and equation of state parameters. We also evaluate the null, weak, and strong energy conditions to assess the traversability of Casimir wormholes. Our primary contribution lies in incorporating the noncommutative model into the analysis and extending the modifications in Casimir energies to the sixth order.