In this paper we study the possibility of sustaining an evolving wormhole via
exotic matter made out of phantom energy. We show that this exotic source can
support the existence of evolving wormhole spacetimes. Explicitly, a family of
evolving Lorentzian wormholes conformally related to another family of
zero-tidal force static wormhole geometries is found in Einstein gravity.
Contrary to the standard wormhole approach, where first a convenient geometry
is fixed and then the matter distribution is derived, we follow the
conventional approach for finding solutions in theoretical cosmology. We derive
an analytical evolving wormhole geometry by supposing that the radial tension
(which is negative to the radial pressure) and the pressure measured in the
tangential directions have barotropic equations of state with constant state
parameters. At spatial infinity this evolving wormhole, supported by this
anisotropic matter, is asymptotically flat, and its slices t= constant are
spaces of constant curvature. During its evolution the shape of the wormhole
expands with constant velocity, i.e without acceleration or deceleration, since
the scale factor has strictly a linear evolution.Comment: 9 pages, 2 figures, Accepted for publication in Phys. Rev.
