Traversable Wormhole Solutions in massive F(T) gravity

We study traversable wormhole geometries in an $F(T)$ teleparallel framework augmented by a perturbative de Rham-Gabadadze-Tolley (dRGT) graviton-mass term. Adopting the static, spherically symmetric Morris-Thorne ansatz, we derive the field and conservation equations and decompose the effective energy-momentum tensor into torsional and massive contributions. Focusing on three representative redshift profiles, namely, constant, logarithmic, and power-law, together with two realizations of the massive sector (the general case and a uniform-pressure specialization), we construct exact, horizonless solutions that satisfy the Morris-Thorne flaring-out condition and are asymptotically flat. The effective matter sector either respects the standard energy conditions or only mildly violates them within controlled parameter ranges. Crucially, the dRGT term supplies an additional anisotropic pressure that can sustain the throat without invoking explicitly exotic matter; in the vanishing-mass limit, the configurations reduce smoothly to standard $F(T)$ wormholes, confirming the internal consistency of the framework.