Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory

Details Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory

2003-03-12

arxiv.org/abs/gr-qc/0303050v1

Gen.Rel.Grav. 35 (2003) 1399-1415

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex-2e, 14 pages, 1 Fig., submitted to GRG

Scientific paper

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 \lambda. After extracting of boundary terms the, so called, "effective matter" part of 5D geometrical action becomes proportional to square of anholonomicity 3-form \lambda\wedge d\lambda. 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 \lambda. 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.

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