Volterra distortions, spinning strings, and cosmic defects

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 linelike 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) ⊃ × T (3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincaré 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 wellknown 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.

Torsion effects on a relativistic position-dependent mass system

“…Now, let us consider a spacetime with a space-like dislocation, where the line element is given in the form [37,38]:…”

Harmonic oscillator in an elastic medium with a spiral dislocation

“…In a crystal, these kinds of defects are related to the presence of curvature and torsion. Another line of research goes to the context of general relativity, where it deals with linear topological defects in the spacetime [4]. The common point between these areas of physics is the description of these defects made by the Volterra process [1,2,4,5].…”

“…Another line of research goes to the context of general relativity, where it deals with linear topological defects in the spacetime [4]. The common point between these areas of physics is the description of these defects made by the Volterra process [1,2,4,5]. Up to now, a great deal of study has explored quantum system in the presence of disclinations [6][7][8][9][10] and screw dislocations [5,[11][12][13][14][15][16] in the context of condensed matter physics.…”

“…In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20]. Moreover, spacetimes with space-like disclinations and with space-like dislocations [4] have also been investigated as backgrounds of relativistic quantum systems [21][22][23][24][25][26][27]. On the hand, studies of an edge dislocation through differential geometry and its influence on quantum systems have not been widely explored.…”

Unconventional stringlike singularities in flat spacetime

“…Another string-like singularity is similar to screw dislocation (see section 2.3). Though the analogy between the spacetime singularities and the defects from the theory of elasticity is delusive sometimes (see section 3.3 and Appendix B) it can be stretched further -Puntigam and Soleng used the Volterra construction to classify the string-like singularities [4]. Which suggests that, vice versa, the properties of string-like singularities might be important in condensed matter physics.…”