Abstract
The objective of this paper is to study static spherically symmetric noncommutative wormhole solutions in the framework of $f(T)$ gravity. We construct $f(T)$ field equations in covariant and effective energy-momentum tensor forms to make a correspondence with general relativity. It is observed that the violation of energy conditions to support the nonstandard wormhole is due to the effective energy-momentum tensor. We explore the noncommutative wormhole solutions for two cases: (i) assume a viable power-law $f(T)$ model to construct the shape function and (ii) a particular shape function is taken to construct the $f(T)$ model. In the first case, only exotic matter forms a wormhole structure in teleparallel gravity, whereas for $f(T)$ gravity, normal matter threads these structures except for a particular range of $r$. For the constructed $f(T)$ model, there does not exist a physically acceptable wormhole solution similar to the teleparallel case.
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