Wormhole

[1] Specifically, they are a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in anti-de Sitter space.

Many scientists postulate that wormholes are merely projections of a fourth spatial dimension, analogous to how a two-dimensional (2D) being could experience only part of a three-dimensional (3D) object.

[9] American theoretical physicist John Archibald Wheeler (inspired by Weyl's work)[9] coined the term "wormhole".

[10][11] In a 1957 paper that he wrote with Charles W. Misner, they write:[12] 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".Wormholes have been defined both geometrically and topologically.

For example, in Enrico Rodrigo's The Physics of Stargates, a wormhole is defined informally as: a region of spacetime containing a "world tube" (the time evolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line (the time evolution of a point or observer).The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the Schwarzschild metric describing an eternal black hole, but it was found that it would collapse too quickly for anything to cross from one end to the other.

[18][19] Einstein–Rosen bridges (or ER bridges),[20] named after Albert Einstein and Nathan Rosen,[21] are connections between areas of space that can be modeled as vacuum solutions to the Einstein field equations, and that are now understood to be intrinsic parts of the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation.

In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region that allows us to extrapolate the trajectories of particles that an outside observer sees rising up away from the event horizon.

[21][25] However, in 1962, John Archibald Wheeler and Robert W. Fuller published a paper[26] showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole.

This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamic variable.

The minimal coupling between torsion and Dirac spinors generates a repulsive spin–spin interaction that is significant in fermionic matter at extremely high densities.

[31] Many physicists, such as Stephen Hawking,[32] Kip Thorne,[33] and others,[34][35][36] argued that such effects might make it possible to stabilize a traversable wormhole.

[37] The only known natural process that is theoretically predicted to form a wormhole in the context of general relativity and quantum mechanics was put forth by Juan Maldacena and Leonard Susskind in their ER = EPR conjecture.

(Ellis specifically rejected referring to the scalar field as 'exotic' because of the antiorthodox coupling, finding arguments for doing so unpersuasive.)

The solution depends on two parameters: m, which fixes the strength of its gravitational field, and n, which determines the curvature of its spatial cross sections.

Kip Thorne and his graduate student Mike Morris independently discovered in 1988 the Ellis wormhole and argued for its use as a tool for teaching general relativity.

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 where the traversing path does not pass through a region of exotic matter.

[46] A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al.,[42] 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.

[38]: 504 To see why exotic matter is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side.

Wormholes might allow effective superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time.

However, in a 1997 paper, Visser hypothesized that a complex "Roman ring" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.

[58] A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the many-worlds interpretation of quantum mechanics.

In 1991 David Deutsch showed that quantum theory is fully consistent (in the sense that the so-called density matrix can be made free of discontinuities) in spacetimes with closed timelike curves.

[60][61] Accordingly, the destructive positive feedback loop of virtual particles circulating through a wormhole time machine, a result indicated by semi-classical calculations, is averted.

[14] Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski's proposal of an Everett phone[62] (named after Hugh Everett) in Steven Weinberg's formulation of nonlinear quantum mechanics.

In the Penrose diagram, an object traveling faster than light will cross the black hole and will emerge from another end into a different space, time or universe.

One type of non-traversable wormhole metric is the Schwarzschild solution (see the first diagram): The original Einstein–Rosen bridge was described in an article published in July 1935.

We call such a connection between the two sheets a "bridge".For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution where

one obtains[68][69] The solution is free from singularities for all finite points in the space of the two sheetsWormholes are a common element in science fiction because they allow interstellar, intergalactic, and sometimes even interuniversal travel within human lifetime scales.