Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach

TL;DR

This paper develops a gauge-invariant 1+3 covariant framework to analyze Weyssenhoff fluid dynamics in general relativity, incorporating spin effects and verifying the resulting equations through specific flow conditions.

Contribution

It provides a novel gauge-invariant dynamical analysis of Weyssenhoff fluids in GR using the 1+3 covariant approach, including constraint verification.

Findings

Derived propagation and constraint equations for Weyssenhoff fluids.

Verified equations for irrotational flow with zero peculiar acceleration.

Established a consistent dynamical framework for spin fluids in GR.

Abstract

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge invariant manner using the 1+3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the constraints.