Dynamic rearrangement of vacuum and the phase transitions in the geometric structure of space-time

TL;DR

This paper explores how spontaneous gauge symmetry breaking can lead to vacuum rearrangements, resulting in phase transitions that produce anisotropic Finslerian space-times with broken isotropy, revealing a complex geometric phase structure.

Contribution

It introduces a classification of metric states and mass shell equations for anisotropic Finslerian spaces arising from vacuum phase transitions.

Findings

Identification of anisotropic condensates causing phase transitions.

Classification of metric states in anisotropic Finslerian spaces.

Analysis of the fine structure of geometric phase transitions.

Abstract

It is shown that in the case of spontaneous breaking of the original gauge symmetry, a dynamic rearrangement of vacuum may lead to the formation of some anisotropic condensates. The appearance of such condensates causes the respective phase transitions in the geometric structure of space-time and creates a flat anisotropic, i.e. Finslerian event space. Actually there arises either a flat relativistically-invariant Finslerian space with partially broken 3D isotropy, i.e. axially-symmetric space, or a flat relativistically-invariant Finslerian space with entirely broken 3D isotropy. The fact that any entirely anisotropic relativistically-invariant Finslerian event space belongs to a 3-parameter family of such spaces gives rise to a fine structure of the respective geometric phase transitions. In the present work the fine structure of the geometric phase transitions is studied by classifying all the metric states of the entirely anisotropic event space and the respective mass shell equations.