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

TL;DR

This paper reveals that classical 5D Kaluza-Klein theory inherently contains nematic-like topological defect structures, linking geometric properties to elastic energy concepts and exploring their physical implications in four-dimensional spacetime.

Contribution

It introduces the concept of nematic dynamics within 5D Kaluza-Klein theory, deriving equilibrium equations and analyzing topological defects from a novel geometric perspective.

Findings

Nematic-like elastic energy is present in 5D geometry.

Derived covariant and 1+4 equilibrium equations.

Discussed physical implications of 5D topological defects.

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 \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.