Historical research guide · 0615 · 2005
Wormholes supported by a phantom energy
Sergey V. Sushkov
In one minute
A wormhole — a tunnel joining two distant regions of space — needs something unusual holding its throat open: matter that pushes outward exactly where gravity would squeeze it shut. Morris and Thorne called that material exotic. Sergey Sushkov, at Kazan State Pedagogical University, points out that cosmology may already have a candidate on the table. Phantom energy is the most extreme form of dark energy, with a pressure more negative than minus its own energy density, and the supernova and microwave-background data of the day did not rule it out. The catch is that dark energy is normally described as spread evenly through the universe, while a wormhole is a lump in spacetime and needs one pressure along the radius and a different one across it. Sushkov extends the definition to a spherically symmetric distribution, shows that such matter satisfies the flare-out condition at a throat automatically, and then writes down exact static wormhole solutions — one with the phantom energy in a bounded shell, one with a smooth Gaussian falloff.
Connection
Chapter 4 needs a source for the exotic matter a traversable wormhole requires, and this paper supplies one that cosmology already argues about rather than one invented for the purpose. It also hands the chapter two facts worth carrying: the exotic material stays bunched near the throat, and from a distance the wormhole’s gravity is indistinguishable from an ordinary positive mass.
From the source
The equation of state used for phantom energy in cosmology, radial pressure equal to w times energy density with w below minus one, can be carried over to an inhomogeneous spherically symmetric configuration by reading the pressure as the radial pressure and letting the transverse pressure follow from the field equations.Section III, Eq. (15)
A spherically symmetric distribution of phantom energy satisfies the flare-out conditions at a wormhole throat automatically: with the throat density fixed at one over eight pi kappa times the throat radius squared, and kappa greater than one, both required inequalities hold.Section III, Eq. (16) with Eqs. (2) and (3)
Two exact static spherically symmetric wormhole solutions supported by phantom energy are constructed: one with constant density confined to a bounded shell around the throat and matched continuously to an exterior Schwarzschild geometry, and one with a smooth Gaussian density profile.Section IV A, Eqs. (17) to (24); Section IV B, Eqs. (25) and (26)
The region holding the phantom energy cannot be made arbitrarily large. In the bounded model its outer radius must stay below a limit r-plus set by the throat radius and the equation-of-state parameter, and in the smooth model the falloff parameter must exceed a critical value that depends on the same parameter, so the exotic matter is effectively confined to the vicinity of the throat.Eq. (19) and footnote; Section IV B, the critical value of alpha; Fig. 3
The asymptotic mass of the phantom-energy wormhole is positive, so a distant observer sees no gravitational difference between the wormhole and an ordinary compact body of the same mass.Eq. (27); Section V, Concluding remarks
Everything here rests on whether the equation-of-state parameter of dark energy really sits below minus one; Sushkov notes that values below minus one are not excluded and are even favoured by the supernova, microwave-background and galaxy-clustering data he cites, which makes the tightening measurement of w the observation that decides whether this material exists to be gathered.Section I, Introduction, opening two paragraphs
The way in
https://doi.org/10.1103/PhysRevD.71.043520How to cite it
Sergey V. Sushkov (2005) Wormholes supported by a phantom energy doi:10.1103/PhysRevD.71.043520