Phantom fluid supporting traversable wormholes in alternative gravity with extra material terms

Wormholes are tunnels connecting different regions in spacetime. They were obtained originally as a solution for Einstein's General Relativity theory and according to this theory, they need to be filled by an exotic kind of an isotropic matter. In the present sense, by "exotic matter", we mean matter that does not satisfy the energy conditions. In this paper, we propose the modeling of wormholes within an alternative gravity theory that proposes an extra material (rather than geometrical) term in its gravitational action. Our solutions are obtained from well-known particular cases of the wormhole metric potentials, named redshift and shape functions, and yield the wormholes to be filled by a phantom fluid, that is, a fluid with equation of state parameter omega < -1. In possession of the solutions for the wormhole material content, we also apply the energy conditions to them. The features of those are carefully discussed.