Phantom fluid wormhole in $f(R,T)$ gravity

Wormholes (WHs) are considered as hypothetical shortcuts or tunnels in spacetime. In general relativity (GR), the fundamental ingredient of WH geometry is the presence of exotic matter at the throat, which is responsible for the violation of null energy condition (NEC). However, the modified gravity theories has shown to be able to provide WH solutions satisfying energy conditions (ECs). In this paper, we study the static spherically symmetric WH solutions in modified $f(R,T)$ gravity for a phantom fluid case. The exact solutions of this model are obtained through the equation of state (EoS), $p=\omega \rho$, associated with phantom dark energy (DE) $\omega<-1$. We find the existence of spherically symmetric WH solution supported by phantom energy distribution. The shape function of the WH is obtained in this model obeys all the WH metric conditions. In modified gravity scenario the phantom fluid WH violates the NEC in radial case, unlike in the tangential case. Furthermore, using the "volume integral quantifier" (VIQ) method, the total amount of EC violating matter in spacetime is discussed briefly.