Casimir Wormholes driven by non-commutative geometries in higher dimensional Einstein Gauss–Bonnet gravity

Abstract

This manuscript investigates the construction of a new class of wormhole solutions motivated by non-commutative geometry in fusion with Casimir wormholes in Einstein Gauss–Bonnet (EGB) gravity . It is not likely to ensure that the violation at small scales is significant enough to produce a macroscopic wormhole by depending merely on the Casimir effect. In our strategy, we solely utilised modifications to the energy–momentum tensor (EMT) in the non-commutative background, coupled with the impact of Casimir phenomena. On the other hand, the Einstein tensor remains unchanged in the Einstein field equations. In this regard, we have assumed four cases of non-commutative effects combined with the Casimir wormholes. We have investigated the non-commutative effects using Gaussian and Lorentzian distributions. Also, we incorporated the Casimir and Generalised Uncertainty Principle (GUP) corrected Casimir wormholes to study the basic features of wormhole solutions. The dynamics of a theory that relates the Gauss–Bonnet (GB) parameters (μ) and non-commutative parameter (β) have been addressed graphically, with a particular focus on analysing null energy conditions (NEC) through contour plots to identify the presence of exotic matter. Furthermore, embedding diagrams have been used to investigate the geometry of newly produced asymptotically flat wormholes. Additionally, the active gravitational mass has been calculated and plotted up to the radius r in the area around the wormhole throat. We have discussed equilibrium conditions to analyse the stability of obtained wormhole solutions. Finally, to understand the complexity of wormhole solutions, we have examined the complexity factor graphically.