Extreme Cosmic String

This paper deals with the geometry of supermassive cosmic strings. We have used an approach that enforces the spacetime of cosmic strings to also satisfy the conservation laws of a cylindric gravitational topological defect, that is a spacetime kink. In the simplest case of kink number unity, the entire energy range of supermassive strings becomes then quantized so that only cylindrical defects with linear energy density $G\mu=1/4$ (critical string) and $G\mu=1/2$ (extreme string) are allowed to occur in this range. It has been seen that the internal spherical coordinate $\theta$ of the string metric embedded in an Euclidean three-space also evolves on imaginary values, leading to the creation of a covering shell of broken phase that protects the core with trapped energy, even for $G\mu=1/2$. Then the conical singularity becomes a removable horizaon singularity. We re-express the extreme string metric in the Finkelstein- McCollum standard form and remove the geodesic incompleteness by using the Kruskal technique. The z=const. sections of the resulting metric are the same as the hemispherical section of the metric of a De Sitter kink. Some physical consequences from these results, including the possibility that the extreme string drives inflation and thermal effects in its core, are also discussed.