Abstract
This study explores new wormhole solutions in the background of teleparallel gravity. All the energy conditions are investigated for two different new calculated shape functions. The presence of exotic matter is confirmed due to the violation of the energy conditions. Thin-shell around the wormhole geometry is obtained by using the cut and paste approach taking the Schwarzschild black hole as an exterior manifold. The stability of thin-shell is explored by using linearized radial perturbation about equilibrium shell radius for both choices of calculated shape functions. It is concluded that stable regions and the position of the expected event horizon depend on the choice of physical parameters.
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