Symmetry evolution for the imperfect fluid under perturbations

TL;DR

This paper investigates how a newly discovered symmetry in imperfect fluids with vorticity evolves under local perturbations, showing that symmetries are temporarily broken but then transformed into new symmetries through tetrad adjustments.

Contribution

It introduces a theorem demonstrating the instantaneous breaking and subsequent evolution of symmetries in imperfect fluids under perturbations, utilizing new tetrads for symmetry realization.

Findings

Symmetries are temporarily broken by local perturbations.

New tetrads enable the realization of evolving symmetries.

Symmetry planes tilt and transform under perturbations.

Abstract

Ever since a new symmetry was found for the imperfect fluid with vorticity the question of the effect of perturbations on the symmetry itself has been raised. This new symmetry arose when realizing that local four-velocity gauge-like transformations would render the left hand side of the Einstein equations invariant. Because the metric tensor would be invariant under this new kind of local transformations. Then the point was raised about the invariance of such a kind of transformations of the stress-energy tensor on the right hand side of the Einstein equations in curved four-dimensional Lorentz spacetimes. It was verified that these invariances do not work with plain perfect fluids but they do work for imperfect fluids. The imperfect fluid stress-energy tensor will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress-energy tensor itself. This local invariance was also the criteria introduced in order to present a new stress-energy tensor for vorticity as well. New tetrads are at the core of the realization of the existence of this new symmetry because it is through these new tetrads that this new symmetry is realized. In this manuscript we will introduce local perturbations by external agents to the relevant objects in the imperfect fluid geometry. We will demonstrate a theorem that proves that the symmetries under four-velocity gauge-like transformations will be instantaneously broken but at the same time transformed into new symmetries. Because the local orthogonal planes determined by these new tetrads, which happen to be the local planes of symmetry will tilt under local perturbations. There will be a symmetry evolution under perturbations.