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 $p_r=ωρ$ 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 $ω<-1$. 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.

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