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.
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