Scalar-tensor teleparallel wormholes by Noether symmetries

A gravitational theory of a scalar field nonminimally coupled with torsion and a boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of the Noether gauge symmetry approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.

Figure 1

Shape function divided by $r$, redshift function and scalar field versus the radial coordinate for $\ell =1$, $I_2=-1.5$, $f_0=-1$ and $r_0=10$

Figure 2

Shape function divided by $r$, redshift function and scalar field versus the radial coordinate for $\ell =1$, $I_2=-3$, $f_0=-1$ and $r_0=10$