Nematic structure of space-time and its topological defects in 5D Kaluza-Klein theory

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 the square of the anholonomicity 3-form lambda boolean AND dlambda. 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 the 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.