Traversable Wormholes in the Conservative $f(R,T)$ Gravity

We present a wormhole construction in the framework of the $f(R,T)$ extended gravity theory, with $R$ being the Ricci curvature scalar and $T$ the trace of the energy-momentum tensor, in the case in which the energy-momentum tensor is conserved. From the conservation equation we find that the $f(R,T)$ function is linear in $T$. By developing the field equations, we find a traversable wormhole that for a range of the model parameter values, has no need to be filled by exotic matter.