Volterra Distortions, Spinning Strings, and Cosmic Defects

TL;DR

This paper explores the analogy between defects in solid materials and spacetime distortions in Einstein-Cartan gravity, systematically constructing distorted spacetimes and identifying matter sources like spin-polarized cosmic strings.

Contribution

It introduces a Poincaré gauge theory framework for distorted spacetimes, extending solid state defect concepts to gravitational models and deriving new solutions with matter sources.

Findings

Constructed all ten possible distorted spacetimes.

Recovered the exterior spacetime of a spin-polarized cosmic string.

Identified matter distributions acting as sources of distorted spacetimes.

Abstract

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.