Exactly solvable model of wormhole supported by phantom energy

TL;DR

This paper presents an exact, solvable model of a wormhole supported by anisotropic phantom energy, featuring non-asymptotically flat spacetime with cosmological horizons and the ability to enclose arbitrary phantom energy amounts.

Contribution

It introduces a new exact solution for a wormhole with anisotropic phantom energy, detailing its geometric properties and energy conditions, and explores its limiting behavior.

Findings

The wormhole solution is exactly solvable and supports anisotropic phantom energy.

The spacetime has cosmological horizons and is not asymptotically flat.

The model allows enclosing arbitrary amounts of phantom energy.

Abstract

We have found a simple exact solution of spherically-symmetrical Einstein equations describing a wormhole for an inhomogeneous distribution of the phantom energy. The equation of state is linear but highly anisotropic: while the radial pressure is negative, the transversal one is positive. At infinity the spacetime is not asymptotically flat and possesses on each side of the bridge a regular cosmological Killing horizon with an infinite area, impenetrable for any particles. This horizon does not arise if the wormhole region is glued to the Schwarzschild region. In doing so, the wormhole can enclose an arbitrary amount of the phantom energy. The configuration under discussion has a limit in which the phantom energy turns into the string dust, the areal radius tends to the constant. In this limit, the strong gravitational mass defect is realized in that the gravitational active mass is finite and constant while the proper mass integrated over the total manifold is infinite.