New symmetry for the imperfect fluid

TL;DR

This paper introduces a new local symmetry for imperfect fluids involving four-velocity gauge-like transformations, leading to invariant stress-energy tensors and potential simplifications in neutron star modeling.

Contribution

It develops a novel tetrad formulation for imperfect fluids with a new symmetry that preserves certain physical quantities under local four-velocity gauge-like transformations.

Findings

Four-velocity curl and metric tensor are invariant under the new transformations.

The imperfect fluid stress-energy tensor can be made invariant with additional variable transformations.

Application to neutron stars demonstrates the practical simplifications achieved.

Abstract

We will address the existence of a new symmetry for an imperfect fluid by introducing local four-velocity gauge-like transformations for the case when there is vorticity. A similar tetrad formulation as to the Einstein-Maxwell spacetimes formalism presented in previous manuscripts will be developed in this manuscript for the imperfect fluids. The four-velocity curl and the metric tensor will be invariant under these kind of four-velocity gauge-like local transformations. While the Einstein-Maxwell stress-energy tensor is locally gauge invariant under electromagnetic gauge transformations, the perfect fluid stress-energy tensor will not be invariant under four-velocity gauge-like local transformations. We will dedicate our analysis to the imperfect fluid stress-energy tensor that 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. We will also pay special attention to the construction of a vorticity stress-energy tensor invariant under local four-velocity gauge-like transformations. An application on neutron stars will be developed in order to show the simplifications brought about by these new tetrads.