Forms of matter and forms of radiation
Abstract
The theory of defects in ordered and ill-ordered media is a well-advanced part of condensed matter physics. Concepts developed in this field also occur in the study of spacetime singularities, namely: i)- the topological theory of quantized defects (Kibble's cosmic strings) and ii)- the Volterra process for continuous defects, used to classify the Poincar\'e symmetry breakings. We reassess the classification of Minkowski spacetime defects in the same theoretical frame, starting from the conjecture that these defects fall into two classes, as on they relate to massive particles or to radiation. This we justify on the empirical evidence of the Hubble's expansion. We introduce timelike and null congruences of geodesics treated as ordered media, viz. 'm'-crystals of massive particles and 'r'-crystals of massless particles, with parallel 4-momenta in M4. Classifying their defects (or 'forms') we find (i) 'm'- and 'r'- Volterra continuous line defects and (ii) quantized topologically stable 'r'-defects, these latter forms being of various dimensionalities. Besides these 'perfect' forms, there are 'imperfect' disclinations that bound misorientation walls in three dimensions. We also speculate on the possible relation of these forms with the large-scale structure of the Universe.