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In physics, a wormhole is a hypothetical topological feature of spacetime that is fundamentally a 'shortcut' through space and time. Spacetime can be viewed as a 2D surface, and when 'folded' over, a wormhole bridge can be formed. A wormhole has at least two mouths which are connected to a single throat or tube. If the wormhole is traversable, matter can 'travel' from one mouth to the other by passing through the throat. While there is no observational evidence for wormholes, spacetimes-containing wormholes are known to be valid solutions in general relativity.

The term wormhole was coined by the American theoretical physicist John Wheeler in 1957. However, the idea of wormholes was theorized already in 1921 by the German mathematician Hermann Weyl in connection with his analysis of mass in terms of electromagnetic field energy.

The name "wormhole" comes from an analogy used to explain the phenomenon. If a worm is travelling over the skin of an apple, then the worm could take a shortcut to the opposite side of the apple's skin by burrowing through its center, rather than travelling the entire distance around, just as a wormhole traveler could take a shortcut to the opposite side of the universe through a topologically nontrivial tunnel.

- If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of nontrivial topology, whose boundary has topology of the form dΣ ~ S
^{2}, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.

Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the space time is simply connected.

Lorentzian wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modeled as vacuum solutions to the Einstein field equations by combining models of a black hole and a white hole. This solution was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through.

Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.

While Schwarzschild wormholes are not traversable, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the 'throat' of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time as well as in space. In a 1988 paper, Morris, Thorne and Yurtsever worked out explicitly how to convert a wormhole traversing space into one traversing time.

It is thought that it may not be possible to convert a wormhole into a time machine in this manner: some analyses using the semiclassical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture. This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps. There is also the Roman ring, which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.

- $ds^2=\; -\; c^2\; dt^2\; +\; dl^2\; +\; (k^2\; +\; l^2)(d\; theta^2\; +\; sin^2\; theta\; ,\; dphi^2)$

One type of non-traversable wormhole metric is the Schwarzschild solution:

- $ds^2=\; -\; c^2\; left(1\; -\; frac\{2GM\}\{rc^2\}right)dt^2\; +\; frac\{dr^2\}\{1\; -\; frac\{2GM\}\{rc^2\}\}\; +\; r^2(d\; theta^2\; +\; sin^2\; theta\; ,\; dphi^2)$

Concept of wormholes is used in The Wild Blue Yonder, a science fiction film by Werner Herzog

Wormholes also play pivotal roles in science fiction where faster-than-light travel is possible though limited, allowing connections between regions that would be otherwise unreachable within conventional timelines. Several examples appear in the Star Trek franchise, including the Bajoran wormhole in the Deep Space Nine series. In Star Trek: The Motion Picture in 1979 the USS Enterprise (NCC-1701) was trapped in a wormhole caused by an imbalance in the calibration of the ship's warp engines when it first achieved warp speed.

In Carl Sagan's novel Contact and subsequent 1997 film starring Jodie Foster and Matthew McConaughey, Foster's character Ellie travels 26 light years through a series of wormholes to the star Vega. The round trip, which to Ellie lasts 18 hours, passes by in a fraction of a second on Earth, making it appear she went nowhere. In her defense, Foster mentions an Einstein-Rosen bridge and tells how she was able to travel faster than light and time. Analysis of the situation by Kip Thorne, on the request of Sagan, is quoted by Thorne as being his original impetus for analyzing the physics of wormholes.

Wormholes play major roles in the television series Farscape, where they are the cause of John Crichton's presence in the alien universe, and in the Stargate series, where stargates create a stable artificial wormhole where matter is disintegrated, converted into energy, and is sent through to be reintegrated at the other side. In the science fiction series Sliders, a wormhole (or vortex, as it is usually called in the show) is used to travel between parallel worlds, and one is seen at least once or twice in every episode. In the pilot episode it was referred to as an "Einstein-Rosen-Podolsky bridge".

The central theme in the movie Donnie Darko revolves around Einstein-Rosen bridges.

Wormholes play a major role in the movie Jumper. The plot revolves around David, a kid who suddenly learns he can teleport himself from one place to another. In the movie, David can only teleport to a place he has been. Once he jumps, the wormhole stays open for a few minutes but is not called a wormhole, David refers to it as a jump scar. NOTE: The other Jumper that David meets does call it a "wormhole" once, when he is angered by David bringing the girl to his secret base in the desert.

In Invader Zim episode "Room With A Moose", Zim tricks his classmates into a wormhole with two exits: a room with a moose (left) and to Earth (right)

In Will Wright's video game Spore, Wormholes play an important part of the space stage. Once the player has obtained a 'wormhole key' they are able to take their ship into wormholes, found scattered across the galaxy, which transport them through a semitransparent blue tunnel (similar to the tunnel seen occasionally in the series Stargate) to exit through another wormhole in some other part of the galaxy. The Galactic Core is also some kind of wormhole which takes the player to what appears to be the center of the universe.

- Metamaterial - substance that can theoretically "construct invisibility cloaks and artificial wormholes
- Black hole
- Faster-than-light
- Krasnikov tube
- Non-orientable wormhole
- Self-consistency principle
- Roman ring

- DeBenedictis, Andrew and Das, A. On a General Class of Wormhole Geometries.
*arXiv eprint server*. . - Dzhunushaliev, Vladimir Strings in the Einstein's paradigm of matter.
*arXiv eprint server*. . - Einstein, Albert and Rosen, Nathan. The Particle Problem in the General Theory of Relativity Physical Review 48, 73 (1935).
- Fuller, Robert W. and Wheeler, John A.. Causality and Multiply-Connected Space-Time Physical Review 128, 919 (1962).
- Garattini, Remo How Spacetime Foam modifies the brick wall.
*arXiv eprint server*. . - González-Díaz, Pedro F. Quantum time machine.
*arXiv eprint server*. . - González-Díaz, Pedro F. Ringholes and closed timelike curves.
*arXiv eprint server*. . - Khatsymosky, Vladimir M. Towards possibility of self-maintained vacuum traversable wormhole.
*arXiv eprint server*. . - Krasnikov, Serguei Counter example to a quantum inequality.
*arXiv eprint server*. . - Krasnikov, Serguei The quantum inequalities do not forbid spacetime shortcuts.
*arXiv eprint server*. . - Li, Li-Xin Two Open Universes Connected by a Wormhole: Exact Solutions.
*arXiv eprint server*. . - Morris, Michael S., Thorne, Kip S., and Yurtsever, Ulvi. Wormholes, Time Machines, and the Weak Energy Condition Physical Review Letters 61, 1446–1449 (1988).
- Morris, Michael S. and Thorne, Kip S.. Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity American Journal of Physics 56, 395-412 (1988).
- Nandi, Kamal K. and Zhang, Yuan-Zhong A Quantum Constraint for the Physical Viability of Classical Traversable Lorentzian Wormholes.
*arXiv eprint server*. . - Ori, Amos A new time-machine model with compact vacuum core.
*arXiv eprint server*. . - Roman, Thomas, A. Some Thoughts on Energy Conditions and Wormholes.
*arXiv eprint server*. . - Teo, Edward Rotating traversable wormholes.
*arXiv eprint server*. . - Visser, Matt The quantum physics of chronology protection by Matt Visser..
*arXiv eprint server*. . An excellent and more concise review. - Visser, Matt. Traversable wormholes: Some simple examples Physical Review D 39, 3182–3184 (1989).

- Creating a Traversable Wormhole by Mohammad Mansouryar
- What exactly is a 'wormhole'? answered by Richard F. Holman, William A. Hiscock and Matt Visser.
- Why wormholes? by Matt Visser.
- Wormholes in General Relativity by Soshichi Uchii.
- New Improved Wormholes by John G. Cramer
- White holes and Wormholes provides a very good description of Schwarzschild wormholes with graphics and animations, by Andrew J. S. Hamilton.
- Questions and Answers about Wormholes a comprehensive wormhole FAQ by Enrico Rodrigo.
- Wormhole on arxiv.org
- - Information about the theory the Large Hadron Collider could create a small wormhole. Possibly making time travel into the past possible.
- animation that simulates traversing a wormhole

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Last updated on Thursday October 09, 2008 at 10:29:06 PDT (GMT -0700)

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Last updated on Thursday October 09, 2008 at 10:29:06 PDT (GMT -0700)

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