Traversable Wormhole Solutions in massive $F(T)$ gravity

TL;DR

This paper explores traversable wormhole solutions within $F(T)$ gravity enhanced by a weak massive graviton term, demonstrating that small graviton masses can support wormholes without exotic matter, and solutions reduce to standard $F(T)$ wormholes when the mass vanishes.

Contribution

It introduces a novel analysis of wormholes in $F(T)$ gravity with a massive graviton, showing how mass effects can sustain wormholes without exotic matter and ensuring consistency with massless limits.

Findings

Wormhole solutions satisfy flaring-out and asymptotic flatness conditions.

Small graviton mass provides anisotropic pressure supporting the wormhole throat.

Solutions reduce smoothly to standard $F(T)$ wormholes as graviton mass approaches zero.

Abstract

We investigate traversable wormhole geometries in the framework of $F(T)$ gravity supplemented by a weak de Rham-Gabadadze-Tolley (dRGT) massive term. Using the static and spherically symmetric Morris-Thorne metric, we derive the field and conservation equations, separating the effective energy-momentum tensor into torsional and massive contributions. We analyze three representative classes of metric redshift functions, namely constant, logarithmic, and power-law forms, and two cases of the massive term, i.e. the general one and the uniform pressure case. The obtained solutions satisfy the flaring-out condition and remain asymptotically flat, while the effective matter sector can fulfill or only mildly violate the standard energy conditions. The results show that the inclusion of a small graviton mass provides an additional anisotropic pressure that can sustain the throat geometry without introducing exotic sources. In the limit of vanishing graviton mass, the configurations continuously reduce to the standard $F(T)$ wormhole solutions, confirming the consistency of the framework.