On Wormholes supported by phantom energy

TL;DR

This paper demonstrates the existence of spherical, asymptotically flat traversable wormholes supported by exotic matter with anisotropic pressures, characterized by linear equations of state, using analytical and numerical methods.

Contribution

It introduces a four-parameter family of wormhole solutions supported by phantom or exotic matter with specific stress tensor properties.

Findings

Existence of wormholes supported by phantom energy.

Solutions have finite ADM mass at both ends.

Parameter restrictions for the stress tensor to support wormholes.

Abstract

By a combination of analytical and numerical techniques, we demonstrate the existence of spherical, asymptotically flat traversable wormholes supported by exotic matter whose stress tensor relative to the orthonormal frame of Killing observers takes the form of a perfect fluid possessing anisotropic pressures and subject to linear equations of state: $\tau=\lambda\rho c^{2}$, $P=\mu\rho c^{2}$. We show that there exists a four parameter family of asymptotically flat spherical wormholes parametrized by the area of the throat A(0), the gradient $\Lambda(0)$ of the red shift factor evaluated at the throat as well as the values of $(\lambda, \mu)$. The latter are subject to restrictions: $\lambda>1$ and $2\mu>\lambda$ or $\lambda<0$ and $2\mu<-|\lambda|$. For particular values of $(\lambda, \mu)$, the stress tensor may be interpreted as representing a phantom configuration, while for other values represents exotic matter. All solutions have the property that the two asymptotically flat ends posses finite ADM mass.