Novel insights into wormhole solutions in extended teleparallel gravity inspired by non-commutative geometry

This paper delves into wormhole solutions in the context of teleparallel Rastall gravity, a special case of [Formula: see text] gravity. We explore wormhole features with respect to the Rastall parameter [Formula: see text] and the coupling parameter [Formula: see text]. In this approach, a spread distribution is used instead of a point-like gravitational source, drawing inspiration from non-commutative geometry. While designing wormhole solutions, two matter density models the Lorentzian, and the Gaussian are taken into account. We prove the flare-out condition and obtain the form function by picking the right constants to meet the Morris–Thorne criterion. The null energy condition is shown to be violated in our study of the energy conditions, which implies the existence of exotic matter required to sustain the wormhole structure. We study the stability of the wormhole model under hydrostatic equilibrium using the Tolman–Oppenheimer–Volkoff equation, where anisotropic, hydrostatic and Rastall forces interact to keep it stable. This research demonstrates that for both Gaussian and Lorentzian matter distributions, traversable wormhole solutions with zero tidal forces are amenable to teleparallel Rastall gravity. As a result of this framework, the asymptotic flatness of spacetime is a result, and the parameters of teleparallel Rastall gravity are highly important in deciding wormhole features.