Wormholes with a barotropic equation of state admitting a one-parameter group of conformal motions

The theoretical construction of a traversable wormhole proposed by Morris and Thorne maintains complete control over the geometry by assigning both the shape and redshift functions, thereby leaving open the determination of the stress–energy tensor. This paper examines the effect of introducing the linear barotropic equation of state p_r=ωρ$p_r=\omega \rho$ on the theoretical construction. If either the energy density or the closely related shape function is known, then the Einstein field equations do not ordinarily yield a finite redshift function. If, however, the wormhole admits a one-parameter group of conformal motions, then both the redshift and shape functions exist provided that −3<ω<−1$-3<\omega <-1$. In a cosmological setting, the equation of state p=ωρ$p=\omega \rho$, ω<−1$\omega <-1$, is associated with phantom dark energy, which is known to support traversable wormholes. The restriction −3<ω<−1$-3<\omega <-1$ that arises in the present wormhole setting can be attributed to the assumption of conformal symmetry.