Modeling phantom energy wormholes from Shan-Chen fluids

In recent years, cosmic observational data have reported that our present universe is undergoing an accelerated expansion, which has been termed as mysterious "dark energy" phenomena, that is, the origin of dark energy has not been determined yet. According to our previous work that a new equation of state \cite{X.Shan and H.Chen1993} can be employed to explain the dark energy, and we are very interested in investigating the astrophysical scale properties of dark energy based on the new cosmological fluids given that the universe is filled with a dark energy fluid everywhere. Hence, in this paper, we study the exact solutions of spherically-symmetrical Einstein field equations describing wormholes supported by phantom energy from Shan-Chen (SC) fluids by considering an obvious relation between the transversal pressure and energy density which is different from our previous work \cite{111}. We have still investigated the important case $\psi\approx1$ which corresponds to the " saturation effect ", and this regime corresponds to an effective form of " asymptotic freedom ", occurring at cosmological rather than subnuclear scales. Then we find out two solutions by making some special choices for the shape function $b(r)$ and discuss the singularities of the solutions and find that the spacetimes are both geodesically incomplete. At the same time, it is worth noting that whether the solutions are geodesically complete or incomplete depends on the appropriate choice of the shape function $b(r)$ through our works. In addition, we match our interior solutions to the exterior Schwarzschild solutions and calculate out the total mass of the wormhole when $r\leq a$.