Nematic Structure of Space-Time and Its Topological Defects in 5D Kaluza-Klein Theory
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 the square of the anholonomicity 3-form λ ∧ 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 the 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.
- Publication:
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General Relativity and Gravitation
- Pub Date:
- August 2003
- DOI:
- 10.1023/A:1024530501257
- arXiv:
- arXiv:gr-qc/0303050
- Bibcode:
- 2003GReGr..35.1399K
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- Latex-2e, 14 pages, 1 Fig., submitted to GRG