Stability and existence of wormhole models in F(Q) gravity generated by holographic dark energy densities

Abstract

In this work, we investigate the existence, stability and physical viability of wormhole solutions within the framework of $F\left(Q\right)$ gravity, a modified gravity theory where $Q$ represents the non-metricity scalar. In this study, we developed wormhole models using holographic dark energy density profiles described by Bekenstein-Hawking and Moradpour, represented as ${\rho }_{bh}\left(r\right)=\frac{{\Psi }_1\pi }{r^2}$ and ${\rho }_M=\frac{{\Psi }_1}{4\pi r^2(\pi \lambda r^2+1)}$, respectively. The derived solutions for the wormhole's shape function fulfil the necessary conditions. This study examines the influence of the parameters ${\Psi }_1$ and ${\Psi }_2$ on the equilibrium state of the wormhole solution and the breaking of energy conditions. Our findings indicate that each model deviates from the null energy condition, indicating the necessity of exotic matter for the stability of wormholes. Additionally, we analysed the geometry of wormhole models by embedding diagrams. To achieve the physical viability of the wormhole, we examined the active gravitational mass ($M_{active}$) for both models.