Deflection angle around generic traversable wormhole solutions and energy conditions in extended teleparallel theory of gravity

Abstract

This study explores traversable wormhole solutions within the framework of $f(T,T)$ gravity, a generalized teleparallel theory that extends $f\left(T\right)$ gravity by incorporating the trace of the energy-momentum tensor $T$. Adopting Weitzenbock geometry, we derive the field equations for a linear $f(T,T)$ model and analyze Morris-Thorne wormhole geometries with two novel shape functions and a fractional redshift function. Violations of the null and strong energy conditions are illustrated, showing the presence of exotic matter near the wormhole throat, while the weak and dominant energy conditions are satisfied. Also, the effective potential for null and timelike geodesics reveals how particle trajectories depend on angular momentum, with deflection angle calculations demonstrating significant light bending near the throat. Numerical results show that increasing parameters in the shape functions enhance energy density and radial pressure violation, whereas larger redshift parameters reduce deflection angles at larger distances. Both shape function models support asymptotically flat and physically viable wormholes, with Model-I exhibiting stronger deflection effects.