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

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)=αQ+β and non-linear f(Q)=Q+mQn 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 α, β, 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. •The field equations of the spherically symmetric wormhole spacetime reserving electromagnetic charge in f(Q) gravity have been developed.•Wormholes were studied within two functional forms of f(Q) gravity under non-commutative background.•For the linear f(Q)=αQ+β gravity, we have successfully obtained the analytical form of shape function for both distributions and studied the behavior of the energy conditions.•For the non-linear f(Q)=Q+mQn gravity, we investigated the behavior of the shape functions and energy conditions by choosing appropriate initial conditions of b(r) for both non-commutative geometries.•Stability analysis was also checked through TOV equations, and through our study, we could conclude that our wormhole solutions are stable.