Some aspects of defect theory in spacetime

TL;DR

This paper classifies spacetime defects called cosmic forms using topological methods, identifying three classes with distinct properties and metrics, and discusses their compatibility with cosmological principles.

Contribution

It introduces a novel classification of 2D defects in 4D spacetime, including the new r-forms related to null rotations, expanding defect theory in cosmology.

Findings

Identifies three classes of cosmic forms: m-, t-, and r-forms.

Provides detailed metrics for each class of cosmic forms.

Shows compatibility of m-forms with space homogeneity and isotropy.

Abstract

The topological theory and the Volterra process are key tools for the classification of defects in Condensed Mater Physics. We employ the same methods to classify the 2D defects of a 4D maximally symmetric spacetime. These \textit{cosmic forms}, which are continuous, fall into three classes: i)- $m$-forms, akin to 3D space disclinations, analogous to Kibble's cosmic strings; ii)- $t$-forms, related to hyperbolic rotations; iii)- $r$-forms, never considered so far, related to null rotations. A detailed account of their metrics is presented. There are \textit{wedge} forms, whose singularities occupy a 2D world sheet, and \textit{twist} forms, whose singularities occupy a 3D world shell. $m$-forms are {compatible} with the cosmological principle of \textit{space} homogeneity and isotropy, $t$- and $r$-forms demand \textit{spacetime} homogeneity. $t$- and $r$-forms are typical of a vacuum obeying the perfect cosmological principle in a de Sitter spacetime. Cosmic forms may assemble into networks generating vanishing curvature.