The Topological Structure of the Space-Time Disclination

TL;DR

This paper explores the topological classification of space-time disclinations using gauge potential decomposition and $$-mapping, revealing their quantized nature and relation to topological invariants like winding number, Brouwer degree, and Hopf index.

Contribution

It introduces a novel topological framework for classifying space-time disclinations via gauge potential decomposition and $$-mapping, linking them to topological invariants.

Findings

Disclinations are composed of self-dual and anti-self-dual curvature parts.

Space-time disclination density projection is topologically quantized.

Disclinations are characterized by winding number, Brouwer degree, and Hopf index.

Abstract

The space-time disclination is studied by making use of the decomposition theory of gauge potential in terms of antisymmetric tensor field and $\phi$-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature compose the space-time disclinations which are classified in terms of topological invariants--winding number. The projection of space-time disclination density along an antisymmetric tensor field is quantized topologically and characterized by Brouwer degree and Hopf index.