Unifying non-commutative geometry with Casimir energy: A novel f(R) wormhole solution

Abstract

A Casimir wormhole is a theoretical concept proposing the negative energy density, generated through the Casimir effect that could support the existence of a traversable wormhole. This article investigates the feasibility of a Casimir wormhole by unifying the Casimir effect and non-commutative geometry within the framework of $f\left(R\right)$ gravity theory using Lorentzian distribution. In this study, we derive the shape function satisfying the throat condition and graphically verify all necessary conditions for a traversable wormhole by varying the gravitational mass μ. In addition to this we examine all the energy conditions and physical properties, to assess the wormhole's stability.