Traversable wormholes with charge and non-commutative geometry in the $f(Q)$ gravity

Abstract: We consider modified symmetric teleparallel gravity (STG), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar $Q$ to study static and spherically symmetric charged traversable wormhole solutions with non-commutative background geometry. The matter source at the wormhole throat is acknowledged to be anisotropic, and the redshift function has a constant value (thus, our wormhole solution is non-tidal). We study the obtained field equations with the two functional forms of $f(Q)$ STG models, such as linear $f(Q)=\alpha Q+\beta$ and non-linear $f(Q)=Q+mQ^n$ models under Gaussian and Lorentzian distributions. Our analysis found the exact wormhole solutions for the linear STG model only. Also, for the non-linear model, we derived numerically suitable forms of wormhole shape functions directly from the modified Einstein Field Equations (EFEs). Besides, we probed these models via Null, Dominant, and Strong energy conditions with respect to free Modified gravity (MOG) parameters $\alpha$, $\beta$, $m$, and $n$. We also used Tolman-Oppenheimer-Vokloff (TOV) equation to investigate the stability of wormhole anisotropic matter in considered MOG. Finally, we plot the equation of state.