Wormhole formations in the galactic halos supported by dark matter models and global monopole charge within $f(Q)$ gravity

This paper discusses the possibility of traversable wormholes in the galactic region supported by dark matter (DM) models and global monopole charge in the context of $f(Q)$ gravity. To understand the features of the wormholes, we comprehensively studied wormhole solutions with various redshift functions under different $f(Q)$ models. We obtained wormhole shape functions for Pseudo Isothermal (PI) and Navarro-Frenk-White (NFW) DM profiles under linear $f(Q)$ gravity. In contrast, we employed an embedding class I approach for the non-linear $f(Q)$ models to investigate wormholes. We noticed that our obtained shape functions satisfy the flare-out conditions under an asymptotic background for each DM profile. Moreover, we checked the energy conditions at the wormhole throat with a radius $r_0$ and noticed the influences of the global monopole’s parameter $\eta$ in the violation of energy conditions, especially null energy conditions. Further, for the non-linear case, we observed that wormhole solutions could not exist for $f(Q)=Q+m{Q}^n$, $f(Q)=Q+\frac{\beta }{Q}$, and $f(Q)={\alpha }_1+{\beta }_1\log (Q)$ under embedding class I approach. Finally, we study the amount of exotic matter via the volume integral quantifier technique for the linear $f(Q)$ model, and we confirm that a small amount of exotic matter is required to sustain the traversable wormholes.