Analogy to a wormhole in a curved 2D space (see Embedding Diagram)

Artist's impression of a wormhole as seen by an observer crossing the event horizon of a Schwarzschild wormhole, which is similar to a Schwarzschild black hole but with the singularity replaced by an unstable path to a white hole in another universe. In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot In Physics, a wormhole is a hypothetical topological feature of Spacetime that is fundamentally a 'shortcut' through Space and Time In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside In Astrophysics, a white hole is the theoretical time reversal of a Black hole. The observer originates from the right, and another universe becomes visible in the center of the wormhole shadow once the horizon is crossed. This new region is, however, unreachable in the case of a Schwarzschild wormhole, as the bridge between the black hole and white hole will always collapse before the observer has time to cross it. See White Holes and Wormholes for a more technical discussion and an animation of what an observer sees when falling into a Schwarzschild wormhole.

In physics, a wormhole is a hypothetical topological feature of spacetime that is basically a 'shortcut' through space and time. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of 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. Matter is commonly defined as being anything that has mass and that takes up space. While there is no observational evidence for wormholes, spacetimes containing wormholes are known to be valid solutions in general relativity. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

The term wormhole was coined by the American theoretical physicist John Wheeler in 1957. Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world John Archibald Wheeler ( July 9, 1911 &ndash April 13, 2008) was an eminent American Theoretical physicist. However, the idea of wormholes was invented already in 1921 by the German mathematician Hermann Weyl in connection with his analysis of mass in terms of electromagnetic field energy. Hermann Klaus Hugo Weyl ( 9 November 1885 – 8 December 1955) was a German Mathematician. The electromagnetic field is a physical field produced by electrically charged objects. ^[1]

This analysis forces one to consider situations. . . where there is a net flux of lines of force through what topologists would call a handle of the multiply-connected space and what physicists might perhaps be excused for more vividly terming a ‘wormhole’.

– John Wheeler in Annals of Physics

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. The apple is the pomaceous Fruit of the apple tree Species Malus domestica in the Rose family Rosaceae. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy

Definition

The basic notion of an intra-universe wormhole is that it is a compact region of spacetime whose boundary is topologically trivial but whose interior is not simply connected. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In Topology, a geometrical object or space is called simply connected (or 1-connected) if it is Path-connected and every path between two points can be Formalizing this idea leads to definitions such as the following, taken from Matt Visser's Lorentzian Wormholes:

If a Lorentzian 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 ~ S², and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS

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.

Wormhole types

Intra-universe wormholes connect one location of a universe to another location of the same universe (in the same present time or unpresent). A wormhole should be able to connect distant locations in the universe by creating a shortcut through spacetime, allowing travel between them that is faster than it would take light to make the journey through normal space. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS See the image above. Inter-universe wormholes connect one universe with another [1], [2]. This gives rise to the speculation that such wormholes could be used to travel from one parallel universe to another. The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, parallel universes, A wormhole which connects (usually closed) universes is often called a Schwarzschild wormhole. The shape of the Universe is an informal name for a subject of investigation within Physical cosmology which describes the Geometry of the Universe In Physics, a wormhole is a hypothetical topological feature of Spacetime that is fundamentally a 'shortcut' through Space and Time Another application of a wormhole might be time travel. This article details time travel itself For other uses see Time Traveler. In that case, it is a shortcut from one point in space and time to another. In string theory, a wormhole has been envisioned to connect two D-branes, where the mouths are attached to the branes and are connected by a flux tube [3]. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named A flux tube is a generally tube-like ( cylindrical) region of space containing a Magnetic field, such that the field at the side surfaces is parallel to them Finally, wormholes are believed to be a part of spacetime foam [4]. Quantum foam, also referred to as spacetime foam, is a concept in Quantum mechanics, devised by John Wheeler in 1955. There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes. Lorentzian wormholes are mainly studied in general relativity and semiclassical gravity, while Euclidean wormholes are studied in particle physics. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Semiclassical gravity is the approximation to the theory of Quantum gravity in which one treats Matter fields as being quantum and the gravitational field Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them Traversable wormholes are a special kind of Lorentzian wormholes which would allow a human to travel from one side of the wormhole to the other. In Physics, a wormhole is a hypothetical topological feature of Spacetime that is fundamentally a 'shortcut' through Space and Time Serguei Krasnikov suggested the term spacetime shortcut as a more general term for (traversable) wormholes and propulsion systems like the Alcubierre drive and the Krasnikov tube to indicate hyperfast interstellar travel. Serguei Vladilenovich Krasnikov (Сергей Владиленович Красников (1961 is a Russian Physicist holding a Ph Spacecraft propulsion is any method used to change the velocity of Spacecraft and artificial Satellites There are many different methods The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of a spacetime exhibiting features reminiscent of The Krasnikov Tube is a speculative mechanism for space travel involving the permanent warping of spacetime into superluminal tunnels

Theoretical basis

It is known that (Lorentzian) wormholes are not excluded within the framework of general relativity, but the physical plausibility of these solutions is uncertain. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 It is also unknown whether a theory of quantum gravity, merging general relativity with quantum mechanics, would still allow them. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Most known solutions of general relativity which allow for traversable wormholes require the existence of exotic matter, a theoretical substance which has negative energy density. Exotic matter is a hypothetical concept of Particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles Energy density is the amount of Energy stored in a given system or region of space per unit Volume, or per unit Mass, depending on the context although However, it has not been mathematically proven that this is an absolute requirement for traversable wormholes, nor has it been established that exotic matter cannot exist.

In March 2005, Amos Ori envisioned a wormhole which allows time travel, does not require any exotic matter and satisfies the weak, dominant, and strong energy conditions [5]. Amos Ori is a professor of Physics at the Technion Israel Institute of Technology in Haifa Israel. In relativistic classical field theories of Gravitation, particularly General relativity, an energy condition is one of various alternative conditions The stability of this solution is uncertain, so it is unclear whether infinite precision would be required for it to form in a way that allows time travel and also whether quantum effects would uphold chronology protection in this case, as analyses using semiclassical gravity have suggested they might do in the case of traversable wormholes. The chronology protection conjecture is a Conjecture by the Physicist Professor Stephen Hawking that the Laws of physics are such as to prevent Semiclassical gravity is the approximation to the theory of Quantum gravity in which one treats Matter fields as being quantum and the gravitational field

Schwarzschild wormholes

Embedded diagram of a Schwarzschild wormhole.

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. A vacuum solution is a solution of a Field equation in which the sources of the field are taken to be identically zero The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e In Astrophysics, a white hole is the theoretical time reversal of a Black hole. This solution was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Prof Nathan Rosen (Hebrew נתן רוזן Born into a Jewish family ( March 22, 1909, Brooklyn, New York &ndash December 18, 1995 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. John Archibald Wheeler ( July 9, 1911 &ndash April 13, 2008) was an eminent American Theoretical physicist. Robert W Fuller (1936 -)earned his PhD in Physics at Princeton University in 1961 and taught at Columbia University where he co-authored

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. A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus.

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). Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in gravitation physics Exotic matter is a hypothetical concept of Particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles

Traversable wormholes

Lorentzian traversable wormholes would allow travel from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris in a 1988 paper; for this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is referred to as a Morris-Thorne wormhole. Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in gravitation physics Mike Morris, aka Michael S Morris, is a physics professor at Butler University. Exotic matter is a hypothetical concept of Particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in which a path through the wormhole can be made in which the traversing path does not pass through a region of exotic matter. Matt Visser is a Mathematics Professor at Victoria University of Wellington. However in the pure Gauss-Bonnet theory exotic matter is not needed in order for wormholes to exist- they can exist even with no matter ^[2] A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al. A cosmic string is a hypothetical 1-dimensional (spatially Topological defect in various fields John G Cramer (born 1934 is a Professor of Physics at the University of Washington in Seattle, U ,^[3], in which it was proposed that such wormholes could have been naturally created in the early universe.

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time as well as in space. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS This article details time travel itself For other uses see Time Traveler. In a 1988 paper, Morris, Thorne and Yurtsever^[4] worked out explicitly how to convert a wormhole traversing space into one traversing time.

Wormholes and faster-than-light travel

Special relativity only applies locally. In Physics, the principle of locality is that distant objects cannot have direct influence on one another an object is influenced directly only by its immediate surroundings Wormholes allow superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole. However, a light beam traveling through the wormhole would always beat the traveler. As an analogy, running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it. You can walk slowly while reaching your destination more quickly because the length of your path is shorter.

Wormholes and time travel

A wormhole could allow time travel. This article details time travel itself For other uses see Time Traveler. ^[4] This could be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial This article discusses a concept in physics For the concept in sociology see Time displacement. In physics the twin paradox is a thought experiment in Special Relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find he However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry. For example, if clocks at both mouths both showed the date as 2000 before one mouth was accelerated, and after being taken on a trip at relativistic velocities the accelerated mouth was brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010, then a traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve. In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. In a Lorentzian manifold, a closed timelike curve (CTC is a Worldline of a material particle in Spacetime that is "closed" returning to its

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. Semiclassical gravity is the approximation to the theory of Quantum gravity in which one treats Matter fields as being quantum and the gravitational field In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty The chronology protection conjecture is a Conjecture by the Physicist Professor Stephen Hawking that the Laws of physics are such as to prevent 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. Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in gravitation physics Black Holes and Time Warps Einstein's Outrageous Legacy (1994 is a Popular science book by Kip Thorne. There is also the Roman ring, which is a configuration of more than one wormhole. A Roman ring, in theoretical Physics, is a configuration of Wormholes where for each individual wormhole the Time difference across its mouths is such that 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. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature

Wormhole metrics

Theories of wormhole metrics describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole metric is the following:

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

Wormholes in fiction

Main article: Wormholes in fiction

Wormholes are a popular feature of science fiction as they allow interstellar (and sometimes interuniversal) travel within human timescales. In the mathematical field of Differential geometry, a metric tensor is a type of function defined on a Manifold (such as a Surface in space In the mathematical field of Differential geometry, a metric tensor is a type of function defined on a Manifold (such as a Surface in space In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside Wormholes are a postulated method within the General theory of relativity, of moving from one point in space to another without crossing the space between It is common for the creators of a fictional universe to decide that faster-than-light travel is either impossible or that the technology does not yet exist, but to use wormholes as a means of allowing humans to travel long distances in short periods. Military science fiction (such as the Wing Commander games) often use a "jump drive" to propel a spacecraft between two fixed "jump points" connecting stellar systems. Wing Commander is a Media franchise consisting of Space combat simulation computer games from Origin Systems Inc Connecting systems in a network like this results in a fixed "terrain" with choke points that can be useful for constructing plots related to military campaigns. The Alderson points used by Larry Niven and Jerry Pournelle in The Mote in God's Eye and related novels are an example, although the mechanism does not seem to describe actual wormhole physics. Laurence van Cott Niven (born April 30, 1938 Los Angeles California) is a US Science fiction author. Jerry Eugene Pournelle (born August 7, 1933) is an American Science fiction Writer, Essayist and Journalist The Mote in God's Eye, by Larry Niven and Jerry Pournelle, is a Science fiction Novel that was first published in 1974 David Weber has also used the device in the Honorverse and other books such as those based upon the Starfire universe. David Mark Weber is an American Science fiction and Fantasy author. Note This is the 'Main' article for the Honor Harrington related Book series and Sub-series by David Weber. Starfire is a Board wargame (a " 4X," eXplore eXpand eXploit and eXterminate simulating Space warfare and empire building in the Naturally occurring wormholes form the basis for interstellar travel in Lois McMaster Bujold's Vorkosigan Saga. Lois McMaster Bujold (born November 2, 1949, Columbus, Ohio) is an American author of Science fiction and Fantasy The Vorkosigan Saga is a series of Science fiction novels and short stories by Lois McMaster Bujold, most of which concern Miles Vorkosigan, a physically They are also used to create an Interstellar Commonwealth in Peter F. Hamilton's Commonwealth Saga. Peter F Hamilton (born 2 March 1960 is a British Science fiction Author. The Commonwealth Saga is a series of Science fiction novels by British science fiction writer Peter F

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. The Wild Blue Yonder is a Science fiction Film by the German director Werner Herzog, released in 2005. Werner Herzog (born Werner H Stipetić; September 5 1942 is a German Film director, Screenwriter, actor and Opera director 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. Star Trek The Motion Picture is a 1979 Science fiction film from Paramount Pictures. The USS Enterprise (NCC-1701 is a Starship in Star Trek, which chronicles the vessel's mission "to explore strange new worlds to

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. Contact is a Science fiction Novel written by Carl Sagan and published in 1985. Contact is a 1997 Science fiction film adapted from the novel by Carl Sagan. Alicia Christian "Jodie" Foster (born November 19 1962 is a two-time Academy Award, BAFTA, and Golden Globe -award winning American Matthew David McConaughey (məˈkɑnəˌheɪ born November 4 1969 is an American Actor. Vega (α Lyr / α Lyrae / Alpha Lyrae ( or) is the brightest Star in the Constellation Lyra, the fifth brightest star in the night The round trip, which to Ellie lasts 18 hours, passes by in a fraction of a second on Earth, making it seem that she didn't go anywhere. 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. Farscape is an American science fiction television series filmed in Australia and produced for the Sci-Fi Channel. Stargate refers to the Science fiction Media franchise owned by MGM that began in 1994 with the Feature film Stargate 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. Sliders is an American Science fiction television series that ran for five seasons from 1995 to 2000. In the pilot episode it was referred to as an "Einstein-Rosen-Podolsky bridge".

A Wormhole is a part of the main back-story in the MMORPG EVE Online, as one allowed the human "species" enter into the galaxy of Eve.

The central theme in the movie Donnie Darko revolves around Einstein-Rosen bridges. Donnie Darko is a 2001 cult classic Psychological thriller Film written and directed by Richard Kelly, and starring

Wormholes play a major role in both the movie and the book series of "Jumper". The plot revolves around David, a kid who suddenly learns he can teleport himself from one place to another. In the book, david can only teleport to a place if he has been there and likewise he can only jump to places he has been in the movie. 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.

See also

• Alcubierre drive
• Black hole
  • Supermassive black hole
  • Micro black hole
  • Intermediate-mass black hole
  • Rotating black hole
• Chronology protection conjecture
• Compact stars
• Faster-than-light
• Gravastar
• Krasnikov Tube
• Neutron star
• Non-orientable wormhole
• Self-consistency principle
• Roman ring
• Schwarzschild metric
• Schwarzschild radius
• Spacecraft propulsion
• String theory
• Theory of relativity
• Time travel
• Timeline of black hole physics
• White hole
• Wormhole switching

References

• DeBenedictis, Andrew and Das, A. . On a General Class of Wormhole Geometries. arXiv eprint server. Retrieved on August 12, 2005.
• Dzhunushaliev, Vladimir. Strings in the Einstein's paradigm of matter. arXiv eprint server. Retrieved on August 12, 2005.
• 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. Retrieved on August 12, 2005.
• González-Díaz, Pedro F. . Quantum time machine. arXiv eprint server. Retrieved on August 12, 2005.
• González-Díaz, Pedro F. . Ringholes and closed timelike curves. arXiv eprint server. Retrieved on August 12, 2005.
• Khatsymosky, Vladimir M. . Towards possibility of self-maintained vacuum traversable wormhole. arXiv eprint server. Retrieved on August 12, 2005.
• Krasnikov, Serguei. Counter example to a quantum inequality. arXiv eprint server. Retrieved on August 12, 2005.
• Krasnikov, Serguei. The quantum inequalities do not forbid spacetime shortcuts. arXiv eprint server. Retrieved on August 12, 2005.
• Li, Li-Xin. Two Open Universes Connected by a Wormhole: Exact Solutions. arXiv eprint server. Retrieved on August 12, 2005.
• 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. Retrieved on August 12, 2005.
• Ori, Amos. A new time-machine model with compact vacuum core. arXiv eprint server. Retrieved on August 12, 2005.
• Roman, Thomas, A. . Some Thoughts on Energy Conditions and Wormholes. arXiv eprint server. Retrieved on August 12, 2005.
• Teo, Edward. Rotating traversable wormholes. arXiv eprint server. Retrieved on August 12, 2005.
• Visser, Matt. The quantum physics of chronology protection by Matt Visser.. arXiv eprint server. Retrieved on August 12, 2005. An excellent and more concise review.
• Visser, Matt. Traversable wormholes: Some simple examples. Physical Review D 39, 3182–3184 (1989).

External links

• 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.
• Wormhole on arxiv.org
• [6] - 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