Wormholes in $f(R,T)$ gravity satisfying the null energy condition with isotropic pressure

Abstract: We consider $f(R, T)$ theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor, to study static spherically symmetric wormhole geometries sustained by matter sources with isotropic pressure. According to restrictions on the wormhole geometries, we carefully adopt different strategies to construct solutions with the properties and characteristics of wormholes. Using a completely general procedure, we provide several examples of wormholes in which the matter threading the wormhole throat satisfies all of the energy conditions and discuss general mechanisms for finding them. Finally, we postulate a smooth transformation for simplifying the nonlinear field equations and have more consistent results than the other ones to conclude that the results can be viewed as specific exact wormhole solutions without the presence of exotic matter.