h i g h l i g h t s• The theoretical construction of Morris-Thorne wormholes retains complete control over the geometry at the expense of the stress-energy tensor.• The introduction of a barotropic equation of state fails to produce a solution even if the energy density is known.• The assumption of conformal symmetry fills the gap in the form of a complete wormhole solution.
a b s t r a c tThe 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 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. In a cosmological setting, the equation of state p = ωρ, ω < −1, is associated with phantom dark energy, which is known to support traversable wormholes.The restriction −3 < ω < −1 that arises in the present wormhole setting can be attributed to the assumption of conformal symmetry.