Matter Geometry Coupling and Casimir Wormhole Geometry

TL;DR

This paper explores traversable wormhole solutions in a modified gravity theory, showing that such wormholes can be stable and do not necessarily require exotic matter that violates energy conditions, unlike in General Relativity.

Contribution

It introduces wormhole solutions within $f(R, ext{L}_m)$ gravity that can be stable and traversable without NEC violation, expanding the possibilities beyond GR.

Findings

Wormholes can be sustained by exotic matter in $f(R, ext{L}_m)$ gravity.

Traversability conditions are satisfied with and without GUP corrections.

Wormholes are shown to be stable under certain equilibrium conditions.

Abstract

In this study, we investigate traversable wormhole solutions within the setup of $f(R,\mathcal{L}_{m})$ gravity, a modified theory of gravity where the gravitational action relies upon the matter Lagrangian $\mathcal{L}_{m}$ and the Ricci scalar $R$. In General Relativity (GR), stability issues in traversable wormholes necessitate the existence of exotic matter that violates the null energy condition (NEC). In contrast, we explore wormhole solutions that align with the criteria for Casimir wormholes, which do not necessarily require NEC violation. Our analysis demonstrates that in the context of $f(R,\mathcal{L}_{m})$ gravity, exotic matter can sustain these wormholes. We further examine the traversability conditions of the wormhole, considering both scenarios with and without the Generalized Uncertainty Principle (GUP) correction. Additionally, the stability of the wormhole is assessed based on equilibrium conditions. Our findings suggest that $f(R,\mathcal{L}_{m})$ gravity offers a viable framework for the existence of stable, traversable wormholes sustained by exotic matter, potentially expanding the landscape of viable wormhole solutions beyond the confines of GR.