Spinning Fluids: A Group Theoretical Approach

TL;DR

This paper develops a group theoretical framework for relativistic non-abelian spinning fluids, deriving equations of motion and exploring applications in cosmology and black hole environments.

Contribution

It introduces a novel group theoretical formulation of spinning fluids and derives a Mathisson-Papapetrou type equation from the de Sitter group.

Findings

Derived a consistent equation for spinning fluids that reduces to non-spinning case

Applied the framework to cosmological models without vorticity

Explored particle dynamics using alternative group theoretical approaches

Abstract

We extend the Lagrangian formulation of relativistic non-abelian fluids in group theory language. We propose a Mathisson-Papapetrou equation for spinning fluids in terms of the reduction limit of de Sitter group. The equation we find correctly boils down to the one for non-spinning fluids. We study the application of our results for an FRW cosmological background for fluids with no vorticity and for dusts in the vicinity of a Kerr black hole. We also explore two alternative approaches based on a group theoretical formulation of particles dynamics.