Exact Analytical Traversable Wormhole Solutions in Teleparallel $F(T)$ Gravity with the de Rham-Gabadadze-Tolley Massive Graviton Sector

Abstract: In this paper, we derive a novel class of exact, static, spherically symmetric traversable wormhole solutions in teleparallel $F(T)$ gravity augmented by the non-linear de Rham-Gabadadze-Tolley (dRGT) graviton mass term. By using the Morris-Thorne ansatz with a generalized redshift function including constant, logarithmic, and power-law profiles, we rigorously integrate the dRGT-modified conservation laws together with the teleparallel field equations to reconstruct both the shape function $b(r)$ and the possible torsion-based teleparallel $F(T)$ solutions. Our solutions, which accommodate both pressureless dust and dark-energy perfect fluids, are naturally expressed via special function representations. We verify the flaring-out condition $b'(r_0)<1$, demonstrate the absence of event horizons, and show that the null and weak energy conditions are either strictly satisfied or incur only controlled violations at the throat. These results establish teleparallel massive gravity as a self-consistent, mathematically rich framework for asymptotically flat wormhole geometries without necessarily invoking an explicit cosmological constant.