Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory
arXiv:gr-qc/0303050 · doi:10.1023/A:1024530501257
Abstract
We show, that classical Kaluza-Klein theory possesses hidden nematic dynamics. It appears as a consequence of 1+4-decomposition procedure, involving 4D observers 1-form λ. After extracting of boundary terms the, so called, "effective matter" part of 5D geometrical action becomes proportional to square of anholonomicity 3-form λ\wedge dλ. It can be interpreted as twist nematic elastic energy, responsible for elastic reaction of 5D space-time on presence of anholonomic 4D submanifold, defined by λ. We derive both 5D covariant and 1+4 forms of 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.
Latex-2e, 14 pages, 1 Fig., submitted to GRG