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 pr=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.