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CONTENTS

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 * (Top)
 * 1Visualization
 * 2Terminology
   Toggle Terminology subsection
   * 2.1Modern definitions
 * 3Development
   Toggle Development subsection
   * 3.1Schwarzschild wormholes
     * 3.1.1Einstein–Rosen bridges
   * 3.2Traversable wormholes
 * 4Raychaudhuri's theorem and exotic matter
 * 5Modified general relativity
 * 6Faster-than-light travel
 * 7Time travel
 * 8Interuniversal travel
 * 9Metrics
 * 10In fiction
 * 11See also
 * 12Notes
 * 13References
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   * 13.1Citations
   * 13.2Sources
 * 14External links

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From Wikipedia, the free encyclopedia

Hypothetical topological feature of spacetime
For other uses, see Wormhole (disambiguation).

General relativity
G μ ν + Λ g μ ν = κ T μ ν {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu
}={\kappa }T_{\mu \nu }}
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A wormhole is a hypothetical structure connecting disparate points in spacetime,
and is based on a special solution of the Einstein field equations.[1]

A wormhole can be visualized as a tunnel with two ends at separate points in
spacetime (i.e., different locations, different points in time, or both).

Wormholes are consistent with the general theory of relativity, but whether
wormholes actually exist remains to be seen. 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.[2] A well-known analogy of such constructs is provided by the Klein
bottle, displaying a hole when rendered in three dimensions but not in four or
higher dimensions.

Theoretically, a wormhole might connect extremely long distances such as a
billion light-years, or short distances such as a few meters, or different
points in time, or even different universes.[3]

In 1995, Matt Visser suggested there may be many wormholes in the universe if
cosmic strings with negative mass were generated in the early universe.[4][5]
Some physicists, such as Kip Thorne, have suggested how to make wormholes
artificially.[6]


VISUALIZATION[EDIT]

Wormhole visualized in 2D

For a simplified notion of a wormhole, space can be visualized as a
two-dimensional surface. In this case, a wormhole would appear as a hole in that
surface, lead into a 3D tube (the inside surface of a cylinder), then re-emerge
at another location on the 2D surface with a hole similar to the entrance. An
actual wormhole would be analogous to this, but with the spatial dimensions
raised by one. For example, instead of circular holes on a 2D plane, the entry
and exit points could be visualized as spherical holes in 3D space leading into
a four-dimensional "tube" similar to a spherinder.[citation needed]

Another way to imagine wormholes is to take a sheet of paper and draw two
somewhat distant points on one side of the paper. The sheet of paper represents
a plane in the spacetime continuum, and the two points represent a distance to
be traveled, but theoretically, a wormhole could connect these two points by
folding that plane (⁠i.e. the paper) so the points are touching. In this way, it
would be much easier to traverse the distance since the two points are now
touching. [citation needed]


TERMINOLOGY[EDIT]

In 1928, German mathematician, philosopher and theoretical physicist Hermann
Weyl proposed a wormhole hypothesis of matter in connection with mass analysis
of electromagnetic field energy;[7][8] however, he did not use the term
"wormhole" (he spoke of "one-dimensional tubes" instead).[9]

American theoretical physicist John Archibald Wheeler (inspired by Weyl's
work)[9] coined the term "wormhole" in a 1957 paper co-authored by Charles W.
Misner:[10]

> 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".
> 
> — Charles Misner and John Wheeler in Annals of Physics


MODERN DEFINITIONS[EDIT]

Wormholes have been defined both geometrically and topologically. [further
explanation needed] From a topological point of view, an intra-universe wormhole
(a wormhole between two points in the same universe) is a compact region of
spacetime whose boundary is topologically trivial, but whose interior is not
simply connected. Formalizing this idea leads to definitions such as the
following, taken from Matt Visser's Lorentzian Wormholes
(1996).[11][page needed]

> If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω
> is of the form Ω ~ S × Σ, where Σ is a three-manifold of the nontrivial
> topology, whose boundary has the topology of the form ∂Σ ~ S2, and if,
> furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains
> a quasi-permanent intrauniverse wormhole.

Geometrically, wormholes can be described as regions of spacetime that constrain
the incremental deformation of closed surfaces. 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).


DEVELOPMENT[EDIT]

"Embedding diagram" of a Schwarzschild wormhole


SCHWARZSCHILD WORMHOLES[EDIT]

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. Wormholes that could be crossed in both directions,
known as traversable wormholes, were thought to be possible only if exotic
matter with negative energy density could be used to stabilize them.[12]
However, physicists later reported that microscopic traversable wormholes may be
possible and not require any exotic matter, instead requiring only electrically
charged fermionic matter with small enough mass that it cannot collapse into a
charged black hole.[13][14] While such wormholes, if possible, may be limited to
transfers of information, humanly traversable wormholes may exist if reality can
broadly be described by the Randall–Sundrum model 2, a brane-based theory
consistent with string theory.[15][16]

EINSTEIN–ROSEN BRIDGES[EDIT]

Einstein–Rosen bridges, also known as EPR=KOI bridges[17] (named after Albert
Einstein and Nathan Rosen),[18] 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. Here, "maximally extended" refers to the idea that the spacetime
should not have any "edges": it should be possible to continue this path
arbitrarily far into the particle's future or past for any possible trajectory
of a free-falling particle (following a geodesic in the spacetime).

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.[19] And just as there are
two separate interior regions of the maximally extended spacetime, there are
also two separate exterior regions, sometimes called two different "universes",
with the second universe allowing us to extrapolate some possible particle
trajectories in the two interior regions. This means that the interior black
hole region can contain a mix of particles that fell in from either universe
(and thus an observer who fell in from one universe might be able to see the
light that fell in from the other one), and likewise particles from the interior
white hole region can escape into either universe. All four regions can be seen
in a spacetime diagram that uses Kruskal–Szekeres coordinates.

In this spacetime, it is possible to come up with coordinate systems such that
if a hypersurface of constant time (a set of points that all have the same time
coordinate, such that every point on the surface has a space-like separation,
giving what is called a 'space-like surface') is picked and an "embedding
diagram" drawn depicting the curvature of space at that time, the embedding
diagram will look like a tube connecting the two exterior regions, known as an
"Einstein–Rosen bridge". The Schwarzschild metric describes an idealized black
hole that exists eternally from the perspective of external observers; a more
realistic black hole that forms at some particular time from a collapsing star
would require a different metric. When the infalling stellar matter is added to
a diagram of a black hole's geography, it removes the part of the diagram
corresponding to the white hole interior region, along with the part of the
diagram corresponding to the other universe.[20]

The Einstein–Rosen bridge was discovered by Ludwig Flamm in 1916,[21] a few
months after Schwarzschild published his solution, and was rediscovered by
Albert Einstein and his colleague Nathan Rosen, who published their result in
1935.[18][22] However, in 1962, John Archibald Wheeler and Robert W. Fuller
published a paper[23] 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. In the
Einstein–Cartan–Sciama–Kibble theory of gravity, however, it forms a regular
Einstein–Rosen bridge. 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. Torsion naturally
accounts for the quantum-mechanical, intrinsic angular momentum (spin) of
matter. The minimal coupling between torsion and Dirac spinors generates a
repulsive spin–spin interaction that is significant in fermionic matter at
extremely high densities. Such an interaction prevents the formation of a
gravitational singularity.[clarification needed] Instead, the collapsing matter
reaches an enormous but finite density and rebounds, forming the other side of
the bridge.[24]

Although Schwarzschild wormholes are not traversable in both directions, 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).[25]

Other non-traversable wormholes include Lorentzian wormholes (first proposed by
John Archibald Wheeler in 1957), wormholes creating a spacetime foam in a
general relativistic spacetime manifold depicted by a Lorentzian manifold,[26]
and Euclidean wormholes (named after Euclidean manifold, a structure of
Riemannian manifold).[27]


TRAVERSABLE WORMHOLES[EDIT]

The Casimir effect shows that quantum field theory allows the energy density in
certain regions of space to be negative relative to the ordinary matter vacuum
energy, and it has been shown theoretically that quantum field theory allows
states where energy can be arbitrarily negative at a given point.[28] Many
physicists, such as Stephen Hawking,[29] Kip Thorne,[30] and others,[31][32][33]
argued that such effects might make it possible to stabilize a traversable
wormhole.[34] 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.
The quantum foam hypothesis is sometimes used to suggest that tiny wormholes
might appear and disappear spontaneously at the Planck scale,[35]: 494–496 [36]
and stable versions of such wormholes have been suggested as dark matter
candidates.[37][38] It has also been proposed that, if a tiny wormhole held open
by a negative mass cosmic string had appeared around the time of the Big Bang,
it could have been inflated to macroscopic size by cosmic inflation.[39]

Image of a simulated traversable wormhole that connects the square in front of
the physical institutes of University of Tübingen with the sand dunes near
Boulogne-sur-Mer in the north of France. The image is calculated with 4D
raytracing in a Morris–Thorne wormhole metric, but the gravitational effects on
the wavelength of light have not been simulated.[note 1]

Lorentzian traversable wormholes would allow travel in both directions 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 in a 1973 paper by Homer
Ellis[40] and independently in a 1973 paper by K. A. Bronnikov.[41] Ellis
analyzed the topology and the geodesics of the Ellis drainhole, showing it to be
geodesically complete, horizonless, singularity-free, and fully traversable in
both directions. The drainhole is a solution manifold of Einstein's field
equations for a vacuum spacetime, modified by inclusion of a scalar field
minimally coupled to the Ricci tensor with antiorthodox polarity (negative
instead of positive). (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. When m is set equal to 0, the drainhole's
gravitational field vanishes. What is left is the Ellis wormhole, a
nongravitating, purely geometric, traversable wormhole.

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.[42] For this reason, the type of traversable wormhole they proposed,
held open by a spherical shell of exotic matter, is also known as a
Morris–Thorne wormhole.

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.
However, in the pure Gauss–Bonnet gravity (a modification to general relativity
involving extra spatial dimensions which is sometimes studied in the context of
brane cosmology) exotic matter is not needed in order for wormholes to
exist—they can exist even with no matter.[43] A type held open by negative mass
cosmic strings was put forth by Visser in collaboration with Cramer et al.,[39]
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. In 1988, Morris, Thorne and
Yurtsever worked out how to convert a wormhole traversing space into one
traversing time by accelerating one of its two mouths.[30] However, according to
general relativity, it would not be possible to use a wormhole to travel back to
a time earlier than when the wormhole was first converted into a time "machine".
Until this time it could not have been noticed or have been used.[35]: 504 


RAYCHAUDHURI'S THEOREM AND EXOTIC MATTER[EDIT]

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. The expansion goes from negative to positive. As the wormhole neck is of
finite size, we would not expect caustics to develop, at least within the
vicinity of the neck. According to the optical Raychaudhuri's theorem, this
requires a violation of the averaged null energy condition. Quantum effects such
as the Casimir effect cannot violate the averaged null energy condition in any
neighborhood of space with zero curvature,[44] but calculations in semiclassical
gravity suggest that quantum effects may be able to violate this condition in
curved spacetime.[45] Although it was hoped recently that quantum effects could
not violate an achronal version of the averaged null energy condition,[46]
violations have nevertheless been found,[47] so it remains an open possibility
that quantum effects might be used to support a wormhole.


MODIFIED GENERAL RELATIVITY[EDIT]

In some hypotheses where general relativity is modified, it is possible to have
a wormhole that does not collapse without having to resort to exotic matter. For
example, this is possible with R2 gravity, a form of f(R) gravity.[48]


FASTER-THAN-LIGHT TRAVEL[EDIT]

Further information: Faster-than-light
Wormhole travel as envisioned by Les Bossinas for NASA, c. 1998

The impossibility of faster-than-light relative speed applies only locally.
Wormholes might allow effective 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 whose length is shorter than the distance
between them outside the wormhole, the time taken to traverse it could 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 same wormhole would beat the traveler.


TIME TRAVEL[EDIT]

Main article: Time travel

If traversable wormholes exist, they might allow time travel.[30] A proposed
time-travel machine using a traversable wormhole might hypothetically work in
the following way: One end of the wormhole is accelerated to some significant
fraction of the speed of light, perhaps with some advanced propulsion system,
and then brought back to the point of origin. Alternatively, another way is to
take one entrance of the wormhole and move it to within the gravitational field
of an object that has higher gravity than the other entrance, and then return it
to a position near the other entrance. For both these methods, time dilation
causes the end of the wormhole that has been moved to have aged less, or become
"younger", than the stationary end as seen by an external observer; however,
time connects differently through the wormhole than outside it, so that
synchronized clocks at either end of the wormhole will always remain
synchronized as seen by an observer passing through the wormhole, no matter how
the two ends move around.[35]: 502  This means that an observer entering the
"younger" end would exit the "older" end at a time when it was the same age as
the "younger" end, effectively going back in time as seen by an observer from
the outside. One significant limitation of such a time machine is that it is
only possible to go as far back in time as the initial creation of the
machine;[35]: 503  it is more of a path through time rather than it is a device
that itself moves through time, and it would not allow the technology itself to
be moved backward in time.[49][50]

According to current theories on the nature of wormholes, construction of a
traversable wormhole would require the existence of a substance with negative
energy, often referred to as "exotic matter". More technically, the wormhole
spacetime requires a distribution of energy that violates various energy
conditions, such as the null energy condition along with the weak, strong, and
dominant energy conditions. However, it is known that quantum effects can lead
to small measurable violations of the null energy condition,[11]: 101  and many
physicists believe that the required negative energy may actually be possible
due to the Casimir effect in quantum physics.[51] Although early calculations
suggested a very large amount of negative energy would be required, later
calculations showed that the amount of negative energy can be made arbitrarily
small.[52]

In 1993, Matt Visser argued that the two mouths of a wormhole with such an
induced clock difference could not be brought together without inducing quantum
field and gravitational effects that would either make the wormhole collapse or
the two mouths repel each other,[53] or otherwise prevent information from
passing through the wormhole.[54] Because of this, the two mouths could not be
brought close enough for causality violation to take place. 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.[55]


INTERUNIVERSAL TRAVEL[EDIT]

See also: Multiverse

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.[56] However, later it was shown that
such a model of closed timelike curves can have internal inconsistencies as it
will lead to strange phenomena like distinguishing non-orthogonal quantum states
and distinguishing proper and improper mixture.[57][58] Accordingly, the
destructive positive feedback loop of virtual particles circulating through a
wormhole time machine, a result indicated by semi-classical calculations, is
averted. A particle returning from the future does not return to its universe of
origination but to a parallel universe. This suggests that a wormhole time
machine with an exceedingly short time jump is a theoretical bridge between
contemporaneous parallel universes.[12]

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[59] (named after Hugh Everett)
in Steven Weinberg's formulation of nonlinear quantum mechanics.[60]

The possibility of communication between parallel universes has been dubbed
interuniversal travel.[61]

Wormhole can also be depicted in a Penrose diagram of a Schwarzschild black
hole. 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. This will be an inter-universal wormhole.


METRICS[EDIT]

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:[62]

d s 2 = − c 2 d t 2 + d ℓ 2 + ( k 2 + ℓ 2 ) ( d θ 2 + sin 2 ⁡ θ d φ 2 ) ,
{\displaystyle ds^{2}=-c^{2}\,dt^{2}+d\ell ^{2}+(k^{2}+\ell ^{2})(d\theta
^{2}+\sin ^{2}\theta \,d\varphi ^{2}),}

first presented by Ellis (see Ellis wormhole) as a special case of the Ellis
drainhole.

One type of non-traversable wormhole metric is the Schwarzschild solution (see
the first diagram):

d s 2 = − c 2 ( 1 − 2 G M r c 2 ) d t 2 + d r 2 1 − 2 G M r c 2 + r 2 ( d θ 2 +
sin 2 ⁡ θ d φ 2 ) . {\displaystyle 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 \,d\varphi ^{2}).}

The original Einstein–Rosen bridge was described in an article published in July
1935.[63][64]

For the Schwarzschild spherically symmetric static solution

d s 2 = − 1 1 − 2 m r d r 2 − r 2 ( d θ 2 + sin 2 ⁡ θ d φ 2 ) + ( 1 − 2 m r ) d
t 2 , {\displaystyle ds^{2}=-{\frac {1}{1-{\frac
{2m}{r}}}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi
^{2})+\left(1-{\frac {2m}{r}}\right)\,dt^{2},}

where d s {\displaystyle ds} is the proper time and c = 1 {\displaystyle c=1} .

If one replaces r {\displaystyle r} with u {\displaystyle u} according to u 2 =
r − 2 m {\displaystyle u^{2}=r-2m}

d s 2 = − 4 ( u 2 + 2 m ) d u 2 − ( u 2 + 2 m ) 2 ( d θ 2 + sin 2 ⁡ θ d φ 2 ) +
u 2 u 2 + 2 m d t 2 {\displaystyle
ds^{2}=-4(u^{2}+2m)\,du^{2}-(u^{2}+2m)^{2}(d\theta ^{2}+\sin ^{2}\theta
\,d\varphi ^{2})+{\frac {u^{2}}{u^{2}+2m}}\,dt^{2}}

> The four-dimensional space is described mathematically by two congruent parts
> or "sheets", corresponding to u > 0 {\displaystyle u>0} and u < 0
> {\displaystyle u<0} , which are joined by a hyperplane r = 2 m {\displaystyle
> r=2m} or u = 0 {\displaystyle u=0} in which g {\displaystyle g} vanishes. We
> call such a connection between the two sheets a "bridge".
> 
> — A. Einstein, N. Rosen, "The Particle Problem in the General Theory of
> Relativity"

For the combined field, gravity and electricity, Einstein and Rosen derived the
following Schwarzschild static spherically symmetric solution

φ 1 = φ 2 = φ 3 = 0 , φ 4 = ε 4 , {\displaystyle \varphi _{1}=\varphi
_{2}=\varphi _{3}=0,\varphi _{4}={\frac {\varepsilon }{4}},}
d s 2 = − 1 ( 1 − 2 m r − ε 2 2 r 2 ) d r 2 − r 2 ( d θ 2 + sin 2 ⁡ θ d φ 2 ) +
( 1 − 2 m r − ε 2 2 r 2 ) d t 2 , {\displaystyle ds^{2}=-{\frac
{1}{\left(1-{\frac {2m}{r}}-{\frac {\varepsilon
^{2}}{2r^{2}}}\right)}}\,dr^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta \,d\varphi
^{2})+\left(1-{\frac {2m}{r}}-{\frac {\varepsilon
^{2}}{2r^{2}}}\right)\,dt^{2},}

where ε {\displaystyle \varepsilon } is the electric charge.

The field equations without denominators in the case when m = 0 {\displaystyle
m=0} can be written

φ μ ν = φ μ , ν − φ ν , μ {\displaystyle \varphi _{\mu \nu }=\varphi _{\mu ,\nu
}-\varphi _{\nu ,\mu }}
g 2 φ μ ν ; σ g ν σ = 0 {\displaystyle g^{2}\varphi _{\mu \nu ;\sigma }g^{\nu
\sigma }=0}
g 2 ( R i k + φ i α φ k α − 1 4 g i k φ α β φ α β ) = 0 {\displaystyle
g^{2}(R_{ik}+\varphi _{i\alpha }\varphi _{k}^{\alpha }-{\frac
{1}{4}}g_{ik}\varphi _{\alpha \beta }\varphi ^{\alpha \beta })=0}

In order to eliminate singularities, if one replaces r {\displaystyle r} by u
{\displaystyle u} according to the equation:

u 2 = r 2 − ε 2 2 {\displaystyle u^{2}=r^{2}-{\frac {\varepsilon ^{2}}{2}}}

and with m = 0 {\displaystyle m=0} one obtains[65][66]

φ 1 = φ 2 = φ 3 = 0 {\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{3}=0} and
φ 4 = ε ( u 2 + ε 2 2 ) 1 / 2 {\displaystyle \varphi _{4}={\frac {\varepsilon
}{\left(u^{2}+{\frac {\varepsilon ^{2}}{2}}\right)^{1/2}}}}
d s 2 = − d u 2 − ( u 2 + ε 2 2 ) ( d θ 2 + sin 2 ⁡ θ d φ 2 ) + ( 2 u 2 2 u 2 +
ε 2 ) d t 2 {\displaystyle ds^{2}=-du^{2}-\left(u^{2}+{\frac {\varepsilon
^{2}}{2}}\right)(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2})+\left({\frac
{2u^{2}}{2u^{2}+\varepsilon ^{2}}}\right)\,dt^{2}}

> The solution is free from singularities for all finite points in the space of
> the two sheets
> 
> — A. Einstein, N. Rosen, "The Particle Problem in the General Theory of
> Relativity"


IN FICTION[EDIT]

Main article: Wormholes in fiction

Wormholes are a common element in science fiction because they allow
interstellar, intergalactic, and sometimes even interuniversal travel within
human lifetime scales. In fiction, wormholes have also served as a method for
time travel.


SEE ALSO[EDIT]

 * Physics portal
 * Star portal

 * Alcubierre drive
 * ER = EPR
 * Gödel metric
 * Krasnikov tube
 * Non-orientable wormhole
 * Novikov self-consistency principle
 * Polchinski's paradox
 * Retrocausality
 * Ring singularity
 * Roman ring


NOTES[EDIT]

 1. ^ Other computer-rendered images and animations of traversable wormholes can
    be seen on this page by the creator of the image in the article, and this
    page has additional renderings.


REFERENCES[EDIT]


CITATIONS[EDIT]

 1.  ^ Overbye, Dennis (10 October 2022). "Black Holes May Hide a Mind-Bending
     Secret About Our Universe – Take gravity, add quantum mechanics, stir. What
     do you get? Just maybe, a holographic cosmos". The New York Times.
     Retrieved 10 October 2022.
 2.  ^ Choi, Charles Q. (2013-12-03). "Spooky physics phenomenon may link
     universe's wormholes". NBC News. Retrieved 2019-07-30.
 3.  ^ "Focus: Wormhole Construction: Proceed with Caution". Physical Review
     Focus. Vol. 2. American Physical Society. 1998-08-03. p. 7.
 4.  ^ Cramer, John; Forward, Robert; Morris, Michael; Visser, Matt; Benford,
     Gregory; Landis, Geoffrey (1995). "Natural wormholes as gravitational
     lenses". Physical Review D. 51 (6): 3117–3120. arXiv:astro-ph/9409051.
     Bibcode:1995PhRvD..51.3117C. doi:10.1103/PhysRevD.51.3117. PMID 10018782.
     S2CID 42837620.
 5.  ^ "Searching for a 'Subway to the Stars'" (Press release). Archived from
     the original on 2012-04-15.
 6.  ^ Thorne, Kip S. (1994). Black holes and time warps : Einstein's outrageous
     legacy. New York. p. 493. ISBN 978-0393312768.{{cite book}}: CS1 maint:
     location missing publisher (link)
 7.  ^ Weyl, H. (1921). "Feld und Materie". Annalen der Physik. 65 (14):
     541–563. Bibcode:1921AnP...370..541W. doi:10.1002/andp.19213701405.
 8.  ^ Scholz, Erhard, ed. (2001). Hermann Weyl's Raum – Zeit – Materie and a
     General Introduction to His Scientific Work. Oberwolfach Seminars. Vol. 30.
     Springer. p. 199. ISBN 9783764364762.
 9.  ^ a b "Hermann Weyl": entry in the Stanford Encyclopedia of Philosophy.
 10. ^ Misner, C. W.; Wheeler, J. A. (1957). "Classical physics as geometry".
     Ann. Phys. 2 (6): 525. Bibcode:1957AnPhy...2..525M.
     doi:10.1016/0003-4916(57)90049-0.
 11. ^ a b Visser, Matt (1996). Lorentzian Wormholes. Springer-Verlag.
     ISBN 978-1-56396-653-8.
 12. ^ a b Rodrigo, Enrico (2010). The Physics of Stargates. Eridanus Press.
     p. 281. ISBN 978-0-9841500-0-7.
 13. ^ "Microscopic wormholes possible in theory". phys.org. Retrieved 22 April
     2021.
 14. ^ Blázquez-Salcedo, Jose Luis; Knoll, Christian; Radu, Eugen (9 March
     2021). "Traversable Wormholes in Einstein-Dirac-Maxwell Theory". Physical
     Review Letters. 126 (10): 101102. arXiv:2010.07317.
     Bibcode:2021PhRvL.126j1102B. doi:10.1103/PhysRevLett.126.101102.
     hdl:10773/32560. PMID 33784127. S2CID 222378921. Retrieved 22 April 2021.
 15. ^ Schirber, Michael (9 March 2021). "Wormholes Open for Transport".
     Physics. Retrieved 22 April 2021.
 16. ^ Maldacena, Juan; Milekhin, Alexey (9 March 2021). "Humanly traversable
     wormholes". Physical Review D. 103 (6): 066007. arXiv:2008.06618.
     Bibcode:2021PhRvD.103f6007M. doi:10.1103/PhysRevD.103.066007. Available
     under CC BY 4.0.
 17. ^ Vladimir Dobrev (ed.), Lie Theory and Its Applications in Physics: Varna,
     Bulgaria, June 2015, Springer, 2016, p. 246.
 18. ^ a b A. Einstein and N. Rosen, "The Particle Problem in the General Theory
     of Relativity," Phys. Rev. 48(73) (1935).
 19. ^ "Black Holes Explained – From Birth to Death". YouTube. Archived from the
     original on 2021-12-11.
 20. ^ "Collapse to a Black Hole". Casa.colorado.edu. 2010-10-03. Retrieved
     2010-11-11. This tertiary source reuses information from other sources but
     does not name them.
 21. ^ Flamm (1916). "Beiträge zur Einsteinschen Gravitationstheorie".
     Physikalische Zeitschrift. XVII: 448. ("Comments on Einstein's Theory of
     Gravity")
 22. ^ Lindley, David (Mar 25, 2005). "Focus: The Birth of Wormholes". Physics.
     15. American Physical Society. Retrieved 20 February 2016.
 23. ^ Fuller, Robert W.; Wheeler, John A. (1962-10-15). "Causality and Multiply
     Connected Space-Time". Physical Review. 128 (2). American Physical Society
     (APS): 919–929. Bibcode:1962PhRv..128..919F. doi:10.1103/physrev.128.919.
     ISSN 0031-899X.
 24. ^ Poplawski, Nikodem J. (2010). "Cosmology with torsion: An alternative to
     cosmic inflation". Phys. Lett. B. 694 (3): 181–185. arXiv:1007.0587.
     Bibcode:2010PhLB..694..181P. doi:10.1016/j.physletb.2010.09.056.
 25. ^ Thorne, Kip S. (1994). Black holes and time warps : Einstein's outrageous
     legacy. New York. p. 488. ISBN 978-0393312768.{{cite book}}: CS1 maint:
     location missing publisher (link)
 26. ^ J. Wheeler (1957). "On the nature of quantum geometrodynamics". Ann.
     Phys. 2 (6): 604–614. Bibcode:1957AnPhy...2..604W.
     doi:10.1016/0003-4916(57)90050-7. (A follow-up paper to Misner and Wheeler
     (December 1957).)
 27. ^ Eduard Prugovecki, Quantum Geometry: A Framework for Quantum General
     Relativity, Springer, 2013, p. 412.
 28. ^ Everett, Allen; Roman, Thomas (2012). Time Travel and Warp Drives.
     University of Chicago Press. p. 167. ISBN 978-0-226-22498-5.
 29. ^ "Space and Time Warps". Hawking.org.uk. Archived from the original on
     2012-02-10. Retrieved 2010-11-11.
 30. ^ a b c Morris, Michael; Thorne, Kip; Yurtsever, Ulvi (1988). "Wormholes,
     Time Machines, and the Weak Energy Condition" (PDF). Physical Review
     Letters. 61 (13): 1446–1449. Bibcode:1988PhRvL..61.1446M.
     doi:10.1103/PhysRevLett.61.1446. PMID 10038800.
 31. ^ Sopova; Ford (2002). "The Energy Density in the Casimir Effect". Physical
     Review D. 66 (4): 045026. arXiv:quant-ph/0204125.
     Bibcode:2002PhRvD..66d5026S. CiteSeerX 10.1.1.251.7471.
     doi:10.1103/PhysRevD.66.045026. S2CID 10649139.
 32. ^ Ford; Roman (1995). "Averaged Energy Conditions and Quantum
     Inequalities". Physical Review D. 51 (8): 4277–4286. arXiv:gr-qc/9410043.
     Bibcode:1995PhRvD..51.4277F. doi:10.1103/PhysRevD.51.4277. PMID 10018903.
     S2CID 7413835.
 33. ^ Olum (1998). "Superluminal travel requires negative energies". Physical
     Review Letters. 81 (17): 3567–3570. arXiv:gr-qc/9805003.
     Bibcode:1998PhRvL..81.3567O. doi:10.1103/PhysRevLett.81.3567.
     S2CID 14513456.
 34. ^ "Newfound Wormhole Allows Information to Escape Black Holes". Quanta
     Magazine. 23 October 2017.
 35. ^ a b c d Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton.
     ISBN 978-0-393-31276-8.
 36. ^ Ian H., Redmount; Wai-Mo Suen (1994). "Quantum Dynamics of Lorentzian
     Spacetime Foam". Physical Review D. 49 (10): 5199–5210.
     arXiv:gr-qc/9309017. Bibcode:1994PhRvD..49.5199R.
     doi:10.1103/PhysRevD.49.5199. PMID 10016836. S2CID 39296197.
 37. ^ Kirillov, A. A.; P. Savelova, E. (2008). "Dark Matter from a gas of
     wormholes". Physics Letters B. 660 (3): 93–99. arXiv:0707.1081.
     Bibcode:2008PhLB..660...93K. doi:10.1016/j.physletb.2007.12.034.
     S2CID 12150385.
 38. ^ Rodrigo, Enrico (2009). "Denouement of a Wormhole-Brane Encounter".
     International Journal of Modern Physics D. 18 (12): 1809–1819.
     arXiv:0908.2651. Bibcode:2009IJMPD..18.1809R.
     doi:10.1142/S0218271809015333. S2CID 119239038.
 39. ^ a b John G. Cramer; Robert L. Forward; Michael S. Morris; Matt Visser;
     Gregory Benford & Geoffrey A. Landis (1995). "Natural Wormholes as
     Gravitational Lenses". Physical Review D. 51 (6): 3117–3120.
     arXiv:astro-ph/9409051. Bibcode:1995PhRvD..51.3117C.
     doi:10.1103/PhysRevD.51.3117. PMID 10018782. S2CID 42837620.
 40. ^ H. G. Ellis (1973). "Ether flow through a drainhole: A particle model in
     general relativity". Journal of Mathematical Physics. 14 (1): 104–118.
     Bibcode:1973JMP....14..104E. doi:10.1063/1.1666161.
 41. ^ K. A. Bronnikov (1973). "Scalar-tensor theory and scalar charge". Acta
     Physica Polonica. B4: 251–266.
 42. ^ Morris, Michael S. & Thorne, Kip S. (1988). "Wormholes in spacetime and
     their use for interstellar travel: A tool for teaching general relativity".
     American Journal of Physics. 56 (5): 395–412. Bibcode:1988AmJPh..56..395M.
     doi:10.1119/1.15620.
 43. ^ Elias Gravanis; Steven Willison (2007). "'Mass without mass' from thin
     shells in Gauss-Bonnet gravity". Phys. Rev. D. 75 (8): 084025.
     arXiv:gr-qc/0701152. Bibcode:2007PhRvD..75h4025G.
     doi:10.1103/PhysRevD.75.084025. S2CID 53529713.
 44. ^ Fewster, Christopher J.; Ken D. Olum; Michael J. Pfenning (2007).
     "Averaged null energy condition in spacetimes with boundaries". Physical
     Review D. 75 (2): 025007. arXiv:gr-qc/0609007. Bibcode:2007PhRvD..75b5007F.
     doi:10.1103/PhysRevD.75.025007. S2CID 119726654.
 45. ^ Visser, Matt (1996). "Gravitational vacuum polarization. II. Energy
     conditions in the Boulware vacuum". Physical Review D. 54 (8): 5116–5122.
     arXiv:gr-qc/9604008. Bibcode:1996PhRvD..54.5116V.
     doi:10.1103/PhysRevD.54.5116. PMID 10021199. S2CID 31954680.
 46. ^ Graham, Noah; Ken D. Olum (2007). "Achronal averaged null energy
     condition". Physical Review D. 76 (6): 064001. arXiv:0705.3193.
     Bibcode:2007PhRvD..76f4001G. doi:10.1103/PhysRevD.76.064001.
     S2CID 119285639.
 47. ^ Urban, Douglas; Ken D. Olum (2010). "Spacetime averaged null energy
     condition". Physical Review D. 81 (6): 124004. arXiv:1002.4689.
     Bibcode:2010PhRvD..81l4004U. doi:10.1103/PhysRevD.81.124004.
     S2CID 118312373.
 48. ^ Duplessis, Francis; Easson, Damien A. (2015). "Exotica ex nihilo:
     Traversable wormholes & non-singular black holes from the vacuum of
     quadratic gravity". Physical Review D. 92 (4): 043516. arXiv:1506.00988.
     Bibcode:2015PhRvD..92d3516D. doi:10.1103/PhysRevD.92.043516.
     S2CID 118307327.
 49. ^ Susskind, Leonard (2005). "Wormholes and Time Travel? Not Likely".
     arXiv:gr-qc/0503097.
 50. ^ Everett, Allen; Roman, Thomas (2012). Time Travel and Warp Drives.
     University of Chicago Press. p. 135. ISBN 978-0-226-22498-5.
 51. ^ Cramer, John G. (1994). "NASA Goes FTL Part 1: Wormhole Physics". Analog
     Science Fiction & Fact Magazine. Archived from the original on June 27,
     2006. Retrieved December 2, 2006.
 52. ^ Visser, Matt; Sayan Kar; Naresh Dadhich (2003). "Traversable wormholes
     with arbitrarily small energy condition violations". Physical Review
     Letters. 90 (20): 201102.1–201102.4. arXiv:gr-qc/0301003.
     Bibcode:2003PhRvL..90t1102V. doi:10.1103/PhysRevLett.90.201102.
     PMID 12785880. S2CID 8813962.
 53. ^ Visser, Matt (1993). "From wormhole to time machine: Comments on
     Hawking's Chronology Protection Conjecture". Physical Review D. 47 (2):
     554–565. arXiv:hep-th/9202090. Bibcode:1993PhRvD..47..554V.
     doi:10.1103/PhysRevD.47.554. PMID 10015609. S2CID 16830951.
 54. ^ Visser, Matt (2002). The quantum physics of chronology protection.
     arXiv:gr-qc/0204022. Bibcode:2003ftpc.book..161V.
 55. ^ Visser, Matt (1997). "Traversable wormholes: the Roman ring". Physical
     Review D. 55 (8): 5212–5214. arXiv:gr-qc/9702043.
     Bibcode:1997PhRvD..55.5212V. doi:10.1103/PhysRevD.55.5212. S2CID 2869291.
 56. ^ Deutsch, David (1991). "Quantum Mechanics Near Closed Timelike Lines".
     Physical Review D. 44 (10): 3197–3217. Bibcode:1991PhRvD..44.3197D.
     doi:10.1103/PhysRevD.44.3197. PMID 10013776.
 57. ^ Brun; et al. (2009). "Localized Closed Timelike Curves Can Perfectly
     Distinguish Quantum States". Physical Review Letters. 102 (21): 210402.
     arXiv:0811.1209. Bibcode:2009PhRvL.102u0402B.
     doi:10.1103/PhysRevLett.102.210402. PMID 19519086. S2CID 35370109.
 58. ^ Pati; Chakrabarty; Agrawal (2011). "Purification of mixed states with
     closed timelike curve is not possible". Physical Review A. 84 (6): 062325.
     arXiv:1003.4221. Bibcode:2011PhRvA..84f2325P.
     doi:10.1103/PhysRevA.84.062325. S2CID 119292717.
 59. ^ Polchinski, Joseph (1991). "Weinberg's Nonlinear quantum Mechanics and
     the Einstein–Podolsky–Rosen Paradox". Physical Review Letters. 66 (4):
     397–400. Bibcode:1991PhRvL..66..397P. doi:10.1103/PhysRevLett.66.397.
     PMID 10043797.
 60. ^ Enrico Rodrigo, The Physics of Stargates: Parallel Universes, Time
     Travel, and the Enigma of Wormhole Physics, Eridanus Press, 2010, p. 281.
 61. ^ Samuel Walker, "Inter-universal travel: I wouldn't start from here, New
     Scientist (1 February 2017).
 62. ^ Raine, Derek; Thomas, Edwin (2009). Black Holes: An Introduction
     (2nd ed.). Imperial College Press. p. 143. doi:10.1142/p637.
     ISBN 978-1-84816-383-6.
 63. ^ Einstein, A.; Rosen, N. (1 July 1935). "The Particle Problem in the
     General Theory of Relativity". Physical Review. 48 (1): 73–77.
     Bibcode:1935PhRv...48...73E. doi:10.1103/PhysRev.48.73.
 64. ^ "Leonard Susskind | "ER = EPR" or "What's Behind the Horizons of Black
     Holes?"". Archived from the original on 2021-12-11 – via www.youtube.com.
 65. ^ "Magnetic 'wormhole' connecting two regions of space created for the
     first time". ScienceDaily.
 66. ^ "Magnetic wormhole created for first time". UAB Barcelona.


SOURCES[EDIT]

 * DeBenedictis, Andrew & Das, A. (2001). "On a General Class of Wormhole
   Geometries". Classical and Quantum Gravity. 18 (7): 1187–1204.
   arXiv:gr-qc/0009072. Bibcode:2001CQGra..18.1187D. CiteSeerX 10.1.1.339.8662.
   doi:10.1088/0264-9381/18/7/304. S2CID 119107035.
 * Dzhunushaliev, Vladimir (2002). "Strings in the Einstein's paradigm of
   matter". Classical and Quantum Gravity. 19 (19): 4817–4824.
   arXiv:gr-qc/0205055. Bibcode:2002CQGra..19.4817D. CiteSeerX 10.1.1.339.1518.
   doi:10.1088/0264-9381/19/19/302. S2CID 976106.
 * Einstein, Albert & Rosen, Nathan (1935). "The Particle Problem in the General
   Theory of Relativity". Physical Review. 48 (1): 73.
   Bibcode:1935PhRv...48...73E. doi:10.1103/PhysRev.48.73.
 * Fuller, Robert W. & Wheeler, John A. (1962). "Causality and
   Multiply-Connected Space-Time". Physical Review. 128 (2): 919.
   Bibcode:1962PhRv..128..919F. doi:10.1103/PhysRev.128.919.
 * Garattini, Remo (2004). "How Spacetime Foam modifies the brick wall". Modern
   Physics Letters A. 19 (36): 2673–2682. arXiv:gr-qc/0409015.
   Bibcode:2004MPLA...19.2673G. doi:10.1142/S0217732304015658. S2CID 119094239.
 * González-Díaz, Pedro F. (1998). "Quantum time machine". Physical Review D. 58
   (12): 124011. arXiv:gr-qc/9712033. Bibcode:1998PhRvD..58l4011G.
   doi:10.1103/PhysRevD.58.124011. hdl:10261/100644. S2CID 28411713.
 * González-Díaz, Pedro F. (1996). "Ringholes and closed timelike curves".
   Physical Review D. 54 (10): 6122–6131. arXiv:gr-qc/9608059.
   Bibcode:1996PhRvD..54.6122G. doi:10.1103/PhysRevD.54.6122. PMID 10020617.
   S2CID 7183386.
 * Khatsymosky, Vladimir M. (1997). "Towards possibility of self-maintained
   vacuum traversable wormhole". Physics Letters B. 399 (3–4): 215–222.
   arXiv:gr-qc/9612013. Bibcode:1997PhLB..399..215K.
   doi:10.1016/S0370-2693(97)00290-6. S2CID 13917471.
 * Krasnikov, Serguei (2006). "Counter example to a quantum inequality". Gravity
   and Cosmology. 46 (2006): 195. arXiv:gr-qc/0409007.
   Bibcode:2006GrCo...12..195K.
 * Krasnikov, Serguei (2003). "The quantum inequalities do not forbid spacetime
   shortcuts". Physical Review D. 67 (10): 104013. arXiv:gr-qc/0207057.
   Bibcode:2003PhRvD..67j4013K. doi:10.1103/PhysRevD.67.104013. S2CID 17498199.
 * Li, Li-Xin (2001). "Two Open Universes Connected by a Wormhole: Exact
   Solutions". Journal of Geometry and Physics. 40 (2): 154–160.
   arXiv:hep-th/0102143. Bibcode:2001JGP....40..154L. CiteSeerX 10.1.1.267.8664.
   doi:10.1016/S0393-0440(01)00028-6. S2CID 44433480.
 * Morris, Michael S.; Thorne, Kip S. & Yurtsever, Ulvi (1988). "Wormholes, Time
   Machines, and the Weak Energy Condition" (PDF). Physical Review Letters. 61
   (13): 1446–1449. Bibcode:1988PhRvL..61.1446M.
   doi:10.1103/PhysRevLett.61.1446. PMID 10038800.
 * Morris, Michael S. & Thorne, Kip S. (1988). "Wormholes in spacetime and their
   use for interstellar travel: A tool for teaching general relativity".
   American Journal of Physics. 56 (5): 395–412. Bibcode:1988AmJPh..56..395M.
   doi:10.1119/1.15620.
 * Nandi, Kamal K. & Zhang, Yuan-Zhong (2006). "A Quantum Constraint for the
   Physical Viability of Classical Traversable Lorentzian Wormholes". Journal of
   Nonlinear Phenomena in Complex Systems. 9 (2006): 61–67. arXiv:gr-qc/0409053.
   Bibcode:2004gr.qc.....9053N.
 * Ori, Amos (2005). "A new time-machine model with compact vacuum core".
   Physical Review Letters. 95 (2): 021101. arXiv:gr-qc/0503077.
   Bibcode:2005PhRvL..95b1101O. doi:10.1103/PhysRevLett.95.021101.
   PMID 16090670.
 * Roman, Thomas A. (2004). "Some Thoughts on Energy Conditions and Wormholes".
   The Tenth Marcel Grossmann Meeting: 1909–1924. arXiv:gr-qc/0409090.
   doi:10.1142/9789812704030_0236. ISBN 978-981-256-667-6. S2CID 18867900.
 * Teo, Edward (1998). "Rotating traversable wormholes". Physical Review D. 58
   (2): 024014. arXiv:gr-qc/9803098. Bibcode:1998PhRvD..58b4014T.
   CiteSeerX 10.1.1.339.966. doi:10.1103/PhysRevD.58.024014. S2CID 15316540.
 * Visser, Matt (2002). "The quantum physics of chronology protection by Matt
   Visser". arXiv:gr-qc/0204022. An excellent and more concise review.
 * Visser, Matt (1989). "Traversable wormholes: Some simple examples". Physical
   Review D. 39 (10): 3182–3184. arXiv:0809.0907. Bibcode:1989PhRvD..39.3182V.
   doi:10.1103/PhysRevD.39.3182. PMID 9959561. S2CID 17949528.


EXTERNAL LINKS[EDIT]

Wikimedia Commons has media related to Wormholes.
 * "What exactly is a 'wormhole'? Have wormholes been proven to exist or are
   they still theoretical??" answered by Richard F. Holman, William A. Hiscock
   and Matt Visser
 * "Why wormholes?" by Matt Visser (October 1996)
 * Wormholes in General Relativity by Soshichi Uchii at the Wayback Machine
   (archived February 22, 2012)
 * Questions and Answers about Wormholes – A comprehensive wormhole FAQ by
   Enrico Rodrigo
 * Large Hadron Collider – Theory on how the collider could create a small
   wormhole, possibly allowing time travel into the past
 * animation that simulates traversing a wormhole
 * Renderings and animations of a Morris-Thorne wormhole
 * NASA's current theory on wormhole creation


 * v
 * t
 * e

Black holes
 * Outline

Types
 * BTZ black hole
 * Schwarzschild
 * Rotating
 * Charged
 * Virtual
 * Kugelblitz
 * Supermassive
 * Primordial
 * Direct collapse
 * Rogue
 * Malament–Hogarth spacetime


Size
 * Micro
   * Extremal
   * Electron
   * Hawking star
 * Stellar
   * Microquasar
 * Intermediate-mass
 * Supermassive
   * Active galactic nucleus
   * Quasar
   * LQG
   * Blazar
   * OVV
   * Radio-Quiet
   * Radio-Loud

Formation
 * Stellar evolution
 * Gravitational collapse
 * Neutron star
   * Related links
 * Tolman–Oppenheimer–Volkoff limit
 * White dwarf
   * Related links
 * Supernova
   * Micronova
   * Hypernova
   * Related links
 * Gamma-ray burst
 * Binary black hole
 * Quark star
 * Supermassive star
 * Quasi-star
 * Supermassive dark star
 * X-ray binary

Properties
 * Astrophysical jet
 * Gravitational singularity
   * Ring singularity
   * Theorems
 * Event horizon
 * Photon sphere
 * Innermost stable circular orbit
 * Ergosphere
   * Penrose process
   * Blandford–Znajek process
 * Accretion disk
 * Hawking radiation
 * Gravitational lens
   * Microlens
 * Bondi accretion
 * M–sigma relation
 * Quasi-periodic oscillation
 * Thermodynamics
 * Bekenstein bound
 * Bousso's holographic bound
   * Immirzi parameter
 * Schwarzschild radius
 * Spaghettification

Issues
 * Black hole complementarity
 * Information paradox
 * Cosmic censorship
 * ER = EPR
 * Final parsec problem
 * Firewall (physics)
 * Holographic principle
 * No-hair theorem

Metrics
 * Schwarzschild (Derivation)
 * Kerr
 * Reissner–Nordström
 * Kerr–Newman
 * Hayward

Alternatives
 * Nonsingular black hole models
 * Black star
 * Dark star
 * Dark-energy star
 * Gravastar
 * Magnetospheric eternally collapsing object
 * Planck star
 * Q star
 * Fuzzball
 * Geon

Analogs
 * Optical black hole
 * Sonic black hole

Lists
 * Black holes
 * Most massive
 * Nearest
 * Quasars
 * Microquasars

Related
 * Outline of black holes
 * Black Hole Initiative
 * Black hole starship
 * Big Bang
 * Big Bounce
 * Compact star
 * Exotic star
   * Quark star
   * Preon star
 * Gravitational waves
 * Gamma-ray burst progenitors
 * Gravity well
 * Hypercompact stellar system
 * Membrane paradigm
 * Naked singularity
 * Population III star
 * Supermassive star
 * Quasi-star
 * Supermassive dark star
 * Rossi X-ray Timing Explorer
 * Superluminal motion
 * Timeline of black hole physics
 * White hole
 * Wormhole
 * Tidal disruption event
 * Planet Nine

Notable
 * Cygnus X-1
 * XTE J1650-500
 * XTE J1118+480
 * A0620-00
 * SDSS J150243.09+111557.3
 * Sagittarius A*
 * Centaurus A
 * Phoenix Cluster
 * PKS 1302-102
 * OJ 287
 * SDSS J0849+1114
 * TON 618
 * MS 0735.6+7421
 * NeVe 1
 * Hercules A
 * 3C 273
 * Q0906+6930
 * Markarian 501
 * ULAS J1342+0928
 * PSO J030947.49+271757.31
 * P172+18

 * Category
 * Commons


 * v
 * t
 * e

Time travel
General terms and concepts
 * Chronology protection conjecture
 * Closed timelike curve
 * Novikov self-consistency principle
 * Self-fulfilling prophecy
 * Quantum mechanics of time travel

Time travel in fiction
 * Timelines in fiction
   * in science fiction
 * Time loop
   * in film

Temporal paradoxes
 * Grandfather paradox
 * Causal loop

Parallel timelines
 * Alternative future
 * Alternate history
 * Many-worlds interpretation
 * Multiverse
 * Parallel universes in fiction

Philosophy of space and time
 * Butterfly effect
 * Determinism
 * Eternalism
 * Fatalism
 * Free will
 * Predestination

Spacetimes in general relativity that
can contain closed timelike curves
 * Alcubierre metric
 * BTZ black hole
 * Gödel metric
 * Kerr metric
 * Krasnikov tube
 * Misner space
 * Tipler cylinder
 * van Stockum dust
 * Traversable wormholes


Authority control databases
National
 * France
 * BnF data
 * Germany
 * Israel
 * United States

Other
 * IdRef

Retrieved from
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Categories:
 * Wormhole theory
 * Albert Einstein
 * Astronomical hypotheses
 * Black holes
 * Conjectures
 * Exotic matter
 * Faster-than-light travel
 * General relativity
 * Gravity
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 * Lorentzian manifolds
 * Space
 * Theory of relativity
 * Time travel

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