Spacetime G-structures I: Topological Defects

TL;DR

This paper explores the mathematical framework of G-structures in spacetime, linking topological defects to physical phenomena and characterizing the spacetime vacuum's wave phase.

Contribution

It introduces a detailed analysis of G-structures in Minkowski space and their topological and geometrical implications for spacetime defects and vacuum phases.

Findings

Characterization of topological defects via G-structures.

Relation of spacetime vacuum wave phase to topological properties.

Mathematical framework connecting geometry with physical spacetime features.

Abstract

The notion of G-structure is defined and various geometrical and topological aspects of such structures are discussed. A particular chain of subgroups in the affine group for Minkowski space is chosen and the canonical geometrical and topological objects that are asssociated with each reduction of the bundle of affine frames on a four-dimensional manifold are detailed. Their physical significance is discussed in the language of topological defects in ordered media. Particular attention is paid to how one topologically characterizes the wave phase of the spacetime vacuum manifold.