Lorentz distributed noncommutative wormhole solutions in extended teleparallel gravity

In this paper, we study static spherically symmetric wormhole solutions in extended teleparallel gravity with the inclusion of noncommutative geometry under a Lorentzian distribution. We obtain expressions of matter components for a non-diagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which impose a condition on the normal matter to satisfy these conditions. We explore the noncommutative wormhole solutions by assuming a viable power-law f(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(T)$$\end{document} and shape function models. For the first model, we discuss two cases in which one leads to teleparallel gravity and the other is for f(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(T)$$\end{document} gravity. The normal matter violates the weak energy condition for the first case, while there exists a possibility for micro physically acceptable wormhole solution. There exists a physically acceptable wormhole solution for the power-law b(r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b(r)$$\end{document} model. Also, we check the equilibrium condition for these solutions, which is only satisfied for the teleparallel case, while for the f(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(T)$$\end{document} case, these solutions are less stable.