Static phantom wormholes of finite size

Abstract

In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate $r$. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state ${p}_{r}/\ensuremath{\rho}<\ensuremath{-}1$, dubbed ``phantom matter.'' Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed of a phantom wormhole connected to an anisotropic spherically symmetric distribution of dark energy. The wormhole part of the full spacetime does not fulfill the dominant energy condition, while the dark energy part does.