2012/04/21 by Maurice Kleman, Kleman, Maurice
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Other Condensed Matter (cond-mat.other) #cond-mat.other #gr-qc
paper · pdf · doi:10.48550/arxiv.1204.4786
22 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1108.2904
arxiv created 2012/04/21 · arxiv updated 2012/04/24
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 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 wedge forms, whose singularities occupy a 2D world sheet, and twist forms, whose singularities occupy a 3D world shell. m-forms are compatible with the cosmological principle of space homogeneity and isotropy, t- and r-forms demand 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.