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|Science| - On Wormholes

Subway to the Stars

From General Relativity it is known that two connected black holes, may allow for apparent FTL travel. These special objects are known as wormholes, which science-fiction most often portrays wrongly. This page gives a brief discussion of wormholes, with an emphasis on The Krasnikov Tube mechanism for "warp drive."

On Wormholes

Stable Wormhole

Wormholes are special case rotating black holes (known as Kerr-type black holes), which can act as apparent FTL (Faster Than Light) tunnels through spacetime. Wormholes exist because the rotating black hole frame drags <http://science.msfc.nasa.gov/newhome/headlines/ast06nov97_1.htm> the internal coordinates of a black hole, resulting in the failure of the collapsed star to produce a singularity. The frame dragged bridge between to black holes are known as the Einstein-Rosen Bridge, this bridge is unstable and is prone to collapse when any material approaches it. However, if there is a sufficient kind of negative energy <http://members.tripod.com/da_theoretical1/wecenergy.html> (or exotic matter), the bridge would remain intact in theory, and recent Cosmological Data <http://members.tripod.com/da_theoretical1/miscinfo.html> suggest that such an energy may exist in some form. The figure on the left shows a stable connected wormhole, with the Einstein-Rosen bridge being held open by exotic matter (the yellow ring).

Wormholes are allowed to exist through a loophole of physics, general relativity <http://members.tripod.com/da_theoretical1/grav.html> is a symmetrical theory, therefore there exist a "white hole," solution for black holes. This white hole is allowed to exist through a negative square root (or imaginary) function of the Schwartzchild metric (a spherically symmetric spacetime). White holes are typically believed to exist within in an imaginary or parallel universe, and there exact nature is not precisely known. It is also not exactly clear as to how the Einstein-Rosen Bridge would connect with other black holes and wormholes (these argument are still rather hot today).

The Krasnikov Tube

The most popular theory for warp drive is the early work pioneered by Miguel Alcubierre <http://members.tripod.com/da_theoretical1/warpsci.html>, however, this work has some rather disappointing aspects. The warp drive proposed by Alcubierre acts to create event horizons (the ring near a black hole, where light can no longer escape) which makes controlling the warp drive from within impossible. However, wormhole type solutions do not have those problems, simply because they include event horizons in there formulation. In 1995 the Russian physcisit S. Krasnikov (gr-qc/9511068 <http://xxx.lanl.gov/abs/gr-qc/9511068>) developed a warp drive like metric, which utilizes these wormholes (given graphically below).

ds^{2=(dt-dx)(dt+k(t,x)dx)}^{The two-dimensional warp drive}

This "warp drive" solution is similar in nature to the Einstien-Rosen Bridge discussed above, and from this it has earned its name the "superlumninal subway." The k(t,x) term represents the area displaced by the "exotic" matter (or negative energy <http://members.tripod.com/da_theoretical1/wecenergy.html>), which is represented by the dark blue, and the apparent FTL region is seen in light blue. Unlike the Alcubierre solution we do not see star light being bent from the spacetime curvature, it is much like traveling through normal space. However, the exotic matter acts to distort space much like projection maps, and therefore makes the return trip seem to go FTL with the right energy conditions. Although the only problem this work seems to have is the "negative energy" requirement, the theory is only two-dimensional, and from Einstein we know that spacetime is at least four-dimensional. In short this theory is far from complete in its description, but offers an intriguing alternative to the Alcubierre Warp Drive.

Other Papers

The Alcubierre paper was the first serious attempt at describing how it may be possible to apparently exceed the speed of light in order to introduce a more realistic model of interstellar travel. However there have been a number of authors who have investigated the possibility of warp drive since the publication of Alcubierre's paper. If you are interested in reading some of the other papers in the field simply click on one of the links below.

The links provided are posted by the Los Alamos National Laboratories E-print Server <http://xxx.lanl.gov/>, for a general search for warp drive given form an abstract of a paper click here <http://arxiv.org/find/gr-qc/1/abs:+AND+warp+drive/0/1/0/all/0/1>.

Complimentary Web Page

If you are further interested in the matematical details of the warp drive I suggest that you visit my sister homepage:

Advanced Warp Physics Homepage <http://members.tripod.com/da_theoretical1/wdphysics.html>

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