### Existence of wormholes with a barotropic equation of state

(0 votes over all institutions)

This paper examines the effect of the linear barotropic equation of state $p=\omega\rho$ on the existence or theoretical construction of traversable wormholes. If either the energy density or the closely related shape function is known, then the resulting redshift function $\Phi$ will almost always lead to an event horizon. Specifying the redshift function avoids this problem but only by relinquishing some of the control over the physics. Moving to a cosmological setting, we assume that $\Phi$ is such that $e^{2\Phi}=[(r+a)/b_0]^l$, $a\ge 0$, based on the existence of galactic rotation curves. Here the wormhole structure can only be maintained if $\omega<-1$. This condition is independent of $l$. The scope of this model can therefore be extended to zero and negative $l$ by taking $l$ to be a convenient parameter that is not necessarily related to the tangential velocity. The main reason is that if $a=0$, then the two special cases $l=0$ and $l<0$ correspond to the only exactly solvable models for wormholes supported by phantom energy, while simultaneously avoiding an event horizon, thereby providing an additional motivation for the form of the redshift function. A final topic is a possible unification of these cases by means of teleparallel gravity.