There are some gravitational theories in which the ordinary energy–momentum conservation law is not valid in the curved space–time. Rastall gravity is one of the known theories in this regard, which includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding traversibility of such wormhole geometry with phantom sources.
