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

TL;DR

This work investigates static, traversable wormhole solutions in massive $F(T)$ gravity augmented by a weak dRGT graviton mass. By employing the Morris–Thorne metric and carefully chosen tetrad/spin-connection pairs, the authors decompose the effective energy–momentum into a cosmological fluid and a massive-gravity sector, then reconstruct $F(T)$ models for constant, logarithmic, and power-law redshift functions. They derive explicit forms for the shape function $b(T)$ and the massive contribution $K_3(T)$, analyzing the flaring-out condition and energy-condition behavior to show that the throat can be supported without exotic matter in many cases, with the massive term acting as an anisotropic pressure. The results connect smoothly to standard $F(T)$ wormholes in the limit $m\to 0$, demonstrating consistency, and reveal rich phenomenology across redshift profiles, including asymptotically flat solutions. These findings highlight the viability of wormholes in a gravity framework that combines torsion-based dynamics with a massive graviton, suggesting further exploration of rotating, time-dependent, or scalar-torsion extensions.

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.

Figures (3)

• Figure 1: The $K_3(T)$ massive function versus $T$ of constant, $a=-1$ and $-2$ logarithmic and $a=1$ and $2$ power-law redshift function cases, for general (upper figures) and uniform pressure (lower figures) massive sources.
• Figure 2: The normalized $F(T)$ versus $T$, of constant, $a=-1$ and $-2$ logarithmic and $a=1$ and $2$ power-law redshift functions. From the top left: $\alpha_{CF}\,\rightarrow\,-1$ limit, $-\frac{2}{3}$, $-\frac{1}{3}$ and $\alpha_{CF}\,\rightarrow\,0$ limit.
• Figure 3: The massive and geometry contributions to teleparallel $F(T)$ solutions versus $T$, of constant, $a=-1$ and $-2$ logarithmic and $a=1$ and $2$ power-law redshift functions, for general (left) and uniform (right) pressure massive sources.