Imprints of Casimir wormhole in Einstein Gauss–Bonnet gravity with non-vanishing complexity factor

Abstract

This article investigates Casimir wormhole solutions in Einstein Gauss–Bonnet (EGB) gravity. We are familiar that Null energy conditions (NEC) need not be satisfied for a stable wormhole due to the existence of exotic matter. As the Casimir effect acts as a negative energy source, it can be treated as a classical applicant for the exotic matter to discuss the stable dynamics of the wormhole. This work explores the Casimir effects with the Generalized Uncertainty Principle (GUP) on wormhole geometry in EGB gravity by confining our results for D=5. We have examined two GUP procedures, e.g., Kempf, Mangano, Mann (KMM) and Dentournay, Gabriel, and Spindel (DGS). We have developed shape functions for Casimir wormholes, and GUP corrected Casimir wormholes and studied their existence. In addition, we investigate the behavior of the Gauss–Bonnet (GB) Coupled parameter and minimal uncertainty (MU) parameter on the Equation of state (EOS) parameter. The active gravitational mass and embedding diagrams for all developed shape functions are analysed. Moreover, the violation of the NEC by an exotic matter, the equilibrium forces, and the complexity factor of Casimir wormholes and GUP-corrected Casimir wormholes have also been explored.