Volterra Distortions, Spinning Strings, and Cosmic Defects

Details Volterra Distortions, Spinning Strings, and Cosmic Defects Volterra Distortions, Spinning Strings, and Cosmic Defects

1996-04-30

arxiv.org/abs/gr-qc/9604057v2

Class.Quant.Grav. 14 (1997) 1129-1149

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Qua

Scientific paper

10.1088/0264-9381/14/5/017

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a $SO(3) {\rlap{$\supset$}\times}} T(3)$ gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.

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