Characterization of wormhole spacetimes supported by a covariant action-dependent Lagrangian theory

In this work, we undertake an analysis of new wormhole solutions within an action-dependent Lagrangian framework. These geometries can be traversable and supported by a positive energy density. The modification of the gravitational field equations is produced by the inclusion in the gravitational Lagrangian linear of a background four-vector ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$. This new term expands significantly the conventional description of gravity making it highly nonlinear, and therefore drawing general conclusions about legitimate forms of ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$ proves a formidable task in general. It is, then, customary to adopt an ansatz that strikes a balance between enabling new phenomenology while retaining a significant degree of generality on ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$. Ours is given by the choice ${\ensuremath{\lambda}}_{\ensuremath{\mu}}=(0,{\ensuremath{\lambda}}_{1}(r),0,0)$, with an arbitrary ${\ensuremath{\lambda}}_{1}(r)$. By setting ${\ensuremath{\lambda}}_{1}(r)=\ensuremath{-}1/r$ we craft new families with physically desirable properties, but the wormholes thus generated turn out to be conical, as evidenced by an angle deficit, in a similar fashion to other known solution families. Under the general shape of ${\ensuremath{\lambda}}_{1}(r)$, we demonstrate that these solutions are not compatible with the null energy condition in general, as it happens to their general relativity counterparts, except on specific occasions where the derivative of the redshift function of the metric diverges at the throat (however, in these latter cases, the traversability of the wormhole will be disrupted). On the other hand, it is possible to solve the conical character and satisfies the flatness condition for more general functions of ${\ensuremath{\lambda}}_{1}(r)$.