New Traversable Wormholes Solutions in $f(T)$ Gravity

TL;DR

This paper investigates dynamical traversable wormhole solutions within $f(T)$ gravity, revealing that such solutions are only possible in static cases and that NEC violation is not essential for their existence.

Contribution

It introduces a new analysis of dynamical wormholes in $f(T)$ gravity using different tetrads, showing static solutions are feasible without NEC violation.

Findings

Dynamical wormholes are only possible as static solutions in $f(T)$ gravity.

NEC violation is not necessary for static traversable wormholes.

Diagonal tetrads constrain $f(T)$ to teleparallel theory, limiting dynamical solutions.

Abstract

In this paper we search for dynamical traversable wormhole solution in the modified $f(T)$ theory of gravity, $T$ being the torsion scalar. For such wormhole, the time dependence is inserted in the static traversable wormhole metric of Morris and Thore. Two set of tetrads are adopted: the diagonal and the non-diagonal tetrads. The diagonal set of tetrads constrains and reduces $f(T)$ model to teleparallel theory where usual solutions have been found. With diagonal set of tetrads, free from the teleparallel theory constraint, our results show that the existence of traversable wormhole is possible only for non-dynamical spacetime metric, i.e, static traversable wormhole solutions. Moreover we take into account energy condition analysis and the results show that the violation of NEC is not determinant for existence of static traversable wormhole solutions.