Editing Cosmic string (section)

===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.