Evolving Lorentzian wormholes supported by phantom matter with constant state parameters

TL;DR

This paper demonstrates that evolving Lorentzian wormholes can be supported by phantom energy with constant state parameters, resulting in a linearly expanding, asymptotically flat spacetime with constant curvature slices.

Contribution

It introduces a new class of evolving wormhole solutions supported by phantom matter with constant barotropic parameters, using a conventional cosmological approach.

Findings

Wormholes are supported by exotic phantom energy with constant state parameters.

The solutions feature linear expansion with constant velocity.

At infinity, the wormhole spacetime is asymptotically flat and of constant curvature.

Abstract

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.