Double gravitational layer traversable wormholes in hybrid metric-Palatini gravity

In this work, we explore the existence of traversable wormhole solutions supported by double gravitational layer thin-shells and satisfying the Null Energy Condition (NEC) throughout the whole spacetime, in a quadratic-linear form of the generalized hybrid metric-Palatini gravity. We start by showing that for a particular quadratic-linear form of the action, the junction conditions on the continuity of the Ricci scalar $R$ and the Palatini Ricci scalar $\mathcal R$ of the theory can be discarded without the appearance of undefined distribution terms in the field equations. As a consequence, a double gravitational layer thin-shell arises at the separation hypersurface. We then outline a general method to find traversable wormhole solutions satisfying the NEC at the throat and provide an example. Finally, we use the previously derived junction conditions to match the interior wormhole solution to an exterior vacuum and asymptotic flat solution, thus obtaining a full traversable wormhole solution supported by a double gravitational layer thin-shell and satisfying the NEC. Unlike the wormhole solutions previously obtained in the scalar-tensor representation of this theory, which were scarce and required fine-tuning, the solutions obtained through this method are numerous and exist for a wide variety of metrics and actions.