Editing Cosmic string (section)

==Gravitation==
{{refimprove section|date=September 2016}}
A string is a geometrical deviation from [[Euclidean geometry]] in spacetime characterized by an angular deficit: a circle around the outside of a string would comprise a total angle less than 360°. <ref>{{cite journal| last=Gott| first=J. Richard| title=Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions| journal=Phys. Rev. Lett.| date=1991| volume=66| issue=9| pages=1126–1129| doi=10.1103/PhysRevLett.66.1126| pmid=10044002| bibcode=1991PhRvL..66.1126G}}</ref> From the [[general theory of relativity]] such a geometrical defect must be in tension, and would be manifested by mass.  Even though cosmic strings are thought to be extremely thin, they would have immense density, and so would represent significant gravitational wave sources. A cosmic string about a kilometer in length may be more massive than the Earth.

However [[general relativity]] predicts that the gravitational potential of a straight string vanishes: there is no gravitational force on static surrounding matter. The only gravitational effect of a straight cosmic string is a relative deflection of matter (or light) passing the string on opposite sides (a purely topological effect). A closed cosmic string gravitates in a more conventional way.{{clarify|date=September 2019}}

During the expansion of the universe, cosmic strings would form a network of loops, and in the past it was thought that their gravity could have been responsible for the original clumping of matter into [[galactic supercluster]]s. It is now calculated that their contribution to the structure formation in the universe is less than 10%.

===Negative mass cosmic string===

The standard model of a cosmic string is a geometrical structure with an angle deficit, which thus is in tension and hence has positive mass. In 1995, [[Matt Visser|Visser]] ''et al.'' proposed that cosmic strings could theoretically also exist with angle excesses, and thus negative tension and hence [[negative mass]]. The stability of such [[exotic matter]] strings is problematic; however, they suggested that if a negative mass string were to be wrapped around a [[wormhole]] in the early universe, such a wormhole could be stabilized sufficiently to exist in the present day.<ref>{{cite journal |arxiv=astro-ph/9409051 |bibcode=1995PhRvD..51.3117C |doi=10.1103/PhysRevD.51.3117 |pmid=10018782 |title=Natural wormholes as gravitational lenses |year=1995 |last1=Cramer |first1=John |last2=Forward |first2=Robert |last3=Morris |first3=Michael |last4=Visser |first4=Matt |last5=Benford |first5=Gregory |last6=Landis |first6=Geoffrey |journal=Physical Review D |volume=51 |issue=6 |pages=3117–3120|s2cid=42837620 }}</ref><ref>{{cite press release |url=http://www.geoffreylandis.com/wormholes.htp |title=Searching for a 'Subway to the Stars' |url-status=dead |archive-url=https://web.archive.org/web/20120415100921/http://www.geoffreylandis.com/wormholes.htp |archive-date=2012-04-15 }}</ref>

===Super-critical cosmic string===
{{refimprove section|date=September 2016}}

The exterior geometry of a (straight) cosmic string can be visualized in an embedding diagram as follows: Focusing on the two-dimensional surface perpendicular to the string, its geometry is that of a cone which is obtained by cutting out a wedge of angle δ and gluing together the edges. The angular deficit δ is linearly related to the string tension (= mass per unit length), i.e. the larger the tension, the steeper the cone. Therefore, δ reaches 2π for a certain critical value of the tension, and the cone degenerates to a cylinder. (In visualizing this setup one has to think of a string with a finite thickness.) For even larger, "super-critical" values, δ exceeds 2π and the (two-dimensional) exterior geometry closes up (it becomes compact), ending in a conical singularity.

However, this static geometry is unstable in the super-critical case (unlike for sub-critical tensions): Small perturbations lead to a dynamical spacetime which expands in axial direction at a constant rate. The 2D exterior is still compact, but the conical singularity can be avoided, and the embedding picture is that of a growing cigar. For even larger tensions (exceeding the critical value by approximately a factor of 1.6), the string cannot be stabilized in radial direction anymore.<ref>{{cite journal|last1=Niedermann|first1=Florian|last2=Schneider|first2=Robert|title=Radially stabilized inflating cosmic strings|journal=Phys. Rev. D|date=2015|volume=91|issue=6|page=064010|doi=10.1103/PhysRevD.91.064010|arxiv = 1412.2750 |bibcode = 2015PhRvD..91f4010N |s2cid=118411378}}</ref>

Realistic cosmic strings are expected to have tensions around 6 orders of magnitude below the critical value, and are thus always sub-critical. However, the inflating cosmic string solutions might be relevant in the context of [[brane cosmology]], where the string is promoted to a 3-[[brane]] (corresponding to our universe) in a six-dimensional bulk.