Editing Wormhole (section)

=== Schwarzschild wormholes ===
<!--'Lorentzian wormhole', 'Lorentzian wormholes', 'Schwarzschild wormhole', 'Lorentzian wormholes', 'Euclidean wormhole', 'Euclidean wormholes', 'Einstein–Rosen bridge', 'Einstein–Rosen bridges', 'Einstein–Rosen bridge', 'Einstein–Rosen bridges', and 'Eternal black hole' redirect here--[[]]''
The equations of the theory of [[general relativity]] have valid solutions that contain wormholes. The first type of wormhole solution discovered was the ''Schwarzschild wormhole''--><!--boldface per WP: R#PLA-->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|traversable wormholes]], were thought to be possible only if [[exotic matter]] with [[negative energy]] [[energy density|density]] could be used to stabilize them.<ref name="Rodrigo2"/> Later, physicists reported that microscopic traversable wormholes may be possible and not require any exotic matter, instead requiring only [[electrically charged]] [[fermion]]ic matter with small enough mass that it cannot collapse into a [[charged black hole]].<ref>{{cite news |title=Microscopic wormholes possible in theory |url=https://phys.org/news/2021-03-microscopic-wormholes-theory.html |access-date=22 April 2021 |work=phys.org |language=en}}</ref><ref>{{cite journal |last1=Blázquez-Salcedo |first1=Jose Luis |last2=Knoll |first2=Christian |last3=Radu |first3=Eugen |title=Traversable Wormholes in Einstein-Dirac-Maxwell Theory |journal=Physical Review Letters |date=9 March 2021 |volume=126 |issue=10 |pages=101102 |doi=10.1103/PhysRevLett.126.101102 |pmid=33784127 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.101102 |access-date=22 April 2021|arxiv=2010.07317 |bibcode=2021PhRvL.126j1102B |hdl=10773/32560 |s2cid=222378921 }}</ref><ref>{{cite journal |last1=Konoplya |first1=R. A. |last2=Zhidenko |first2=A. |title=Traversable Wormholes in General Relativity |journal=Physical Review Letters |date=4 March 2022 |volume=128 |issue=9 |pages=091104 |doi=10.1103/PhysRevLett.128.091104 |pmid=35302821 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.091104 |arxiv=2106.05034 |bibcode=2022PhRvL.128i1104K |s2cid=247245028 }}</ref> 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|Randall–Sundrum model 2]], a [[brane]]-based theory consistent with [[string theory]].<ref>{{cite news |last1=Schirber |first1=Michael |title=Wormholes Open for Transport |url=https://physics.aps.org/articles/v14/s28 |access-date=22 April 2021 |work=Physics |date=9 March 2021 |language=en}}</ref><ref>{{cite journal |last1=Maldacena |first1=Juan |last2=Milekhin |first2=Alexey |title=Humanly traversable wormholes |journal=Physical Review D |date=9 March 2021 |volume=103 |issue=6 |pages=066007 |doi=10.1103/PhysRevD.103.066007 |arxiv=2008.06618 |bibcode=2021PhRvD.103f6007M |doi-access=free }} [[File:CC-BY icon.svg|50px]] Available under [https://creativecommons.org/licenses/by/4.0/ CC BY 4.0].</ref>

==== Einstein–Rosen bridges ====
'''Einstein–Rosen bridges''' (or '''ER bridges'''),<ref name="Dobrev">Vladimir Dobrev (ed.), ''Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2015'', Springer, 2016, p. 246.</ref> named after [[Albert Einstein]] and [[Nathan Rosen]],<ref name=ER/> are connections between areas of space that can be modeled as [[vacuum solution]]s to the [[Einstein field equations]], and that are now understood to be intrinsic parts of the [[Kruskal–Szekeres coordinates#The maximally extended Schwarzschild solution|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 [[Geodesics_in_general_relativity|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.<ref>{{Cite web|title=Black Holes Explained – From Birth to Death|url=https://www.youtube.com/watch?v=9P6rdqiybaw |archive-url=https://ghostarchive.org/varchive/youtube/20211211/9P6rdqiybaw |archive-date=2021-12-11 |url-status=live|website=[[YouTube]]| date=12 August 2018 }}{{cbignore}}</ref> 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 system]]s 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.<ref>{{cite web|url=http://casa.colorado.edu/~ajsh/collapse.html#kruskal |title=Collapse to a Black Hole |publisher=Casa.colorado.edu |date=2010-10-03 |access-date=2010-11-11}}{{tertiary source|date=June 2023}}</ref>

The Einstein–Rosen bridge was discovered by [[Ludwig Flamm]] in 1916,<ref>{{Cite journal|last=Flamm|title=Beiträge zur Einsteinschen Gravitationstheorie|date=1916|journal=[[Physikalische Zeitschrift]]|volume=XVII|page=448}} ("Comments on Einstein's Theory of Gravity")</ref> 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.<ref name=ER>A. Einstein and N. Rosen, "The Particle Problem in the General Theory of Relativity," ''Phys. Rev.'' '''48'''(73) (1935).</ref><ref name="focus032505">{{cite journal|last1=Lindley|first1=David|title=Focus: The Birth of Wormholes|url=http://physics.aps.org/story/v15/st11|journal=Physics|publisher=American Physical Society|access-date=20 February 2016|date=Mar 25, 2005|volume=15}}</ref> In 1962, [[John Archibald Wheeler]] and [[Robert W. Fuller]] published a paper<ref>{{cite journal |last1=Fuller |first1=Robert W. |last2=Wheeler |first2=John A. |title=Causality and Multiply Connected Space-Time |journal=Physical Review |publisher=American Physical Society (APS) |volume=128 |issue=2 |date=1962-10-15 |issn=0031-899X |doi=10.1103/physrev.128.919 |pages=919–929 |bibcode=1962PhRv..128..919F }}</ref> 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 theory|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 (physics)|spin]]) of matter. The minimal coupling between torsion and [[Dirac spinor]]s 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 (e.g. a black hole). Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.<ref>{{cite journal |author=Poplawski, Nikodem J. |author-link=Nikodem Popławski |year=2010 |title=Cosmology with torsion: An alternative to cosmic inflation |journal=Phys. Lett. B |volume=694 |issue=3 |pages=181–185 |doi=10.1016/j.physletb.2010.09.056|arxiv = 1007.0587 |bibcode = 2010PhLB..694..181P }}</ref>

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).<ref>{{cite book |last1=Thorne |first1=Kip S. |title=Black holes and time warps : Einstein's outrageous legacy |date=1994 |location=New York |isbn=978-0393312768 |page=488}}</ref>

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]],<ref>{{cite journal |author=J. Wheeler |title=On the nature of quantum geometrodynamics |journal=Ann. Phys. |date=1957 |volume=2 |issue=6 |pages=604–614 |doi=10.1016/0003-4916(57)90050-7|bibcode = 1957AnPhy...2..604W }} (A follow-up paper to Misner and Wheeler (December 1957).)</ref> and ''Euclidean wormholes'' (named after [[Euclidean manifold]], a structure of [[Riemannian manifold]]).<ref>Eduard Prugovecki, ''Quantum Geometry: A Framework for Quantum General Relativity'', Springer, 2013, p. 412.</ref>