Lorentz Distributed Noncommutative Wormhole Solutions in Extended Teleparallel Gravity

TL;DR

This paper investigates static spherically symmetric wormhole solutions within extended teleparallel gravity incorporating noncommutative geometry, analyzing energy conditions, stability, and specific models of $f(T)$ and shape functions.

Contribution

It introduces new wormhole solutions in extended teleparallel gravity with noncommutative geometry, exploring their physical viability and stability under different models.

Findings

Normal matter can satisfy energy conditions in certain models.

Some wormhole solutions are physically acceptable and stable.

Solutions vary in stability between teleparallel and $f(T)$ gravity.

Abstract

In this paper, we study static spherically symmetric wormhole solutions in extended teleparallel gravity with the inclusion of noncommutative geometry under Lorentzian distribution. We obtain expressions of matter components for non-diagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which impose condition on the normal matter to satisfy these conditions. We explore the noncommutative wormhole solutions by assuming a viable power-law $f(T)$ and shape function models. For the first model, we discuss two cases in which one leads to teleparallel gravity and other is for $f(T)$ gravity. The normal matter violates the weak energy condition for first case while there exist a possibility for micro physically acceptable wormhole solution. There exist a physically acceptable wormhole solution for the power-law $b(r)$ model. Also, we check the equilibrium condition for these solutions which is only satisfied for teleparallel case while for $f(T)$ case, these solutions are less stable.