Wormholes in $f(T,\mathcal{T})$ gravity

Abstract: This study aims to investigate the physical properties of wormhole geometry within the context of $f(T,\mathcal{T})$ gravity, which serves as a teleparallel formulation of general relativity. We study a linear model, $f(T,\mathcal{T})=\alpha T+\beta\mathcal{T}$, to explore traversable wormholes. A linear equation of state is utilized for radial pressure, leading to a power-law shaped function. It was found that the violation of energy conditions, depends on the $\alpha$ and $\beta$ parameters. A diverse array of intriguing wormhole solutions was identified, contingent upon the specific model parameters employed. It is demonstrated that isotropic wormhole solutions cannot be attained within this framework. Additionally, solutions characterized by a variable equation of state parameter are introduced. A comparative analysis of wormhole solutions in the context of $f(T,\mathcal{T})$ and curvature-based gravity, specifically $f(R,T)$, is also provided.