Causality of polarizeable dissipative fluids from Lagrangian hydrodynamics

TL;DR

This paper analyzes the causality constraints in hydrodynamics with spin, viscosity, and polarization, revealing how their interplay affects dispersion relations and phenomenological implications.

Contribution

It introduces a causality analysis incorporating spin, viscosity, and polarization relaxation times, revealing their combined effects on hydrodynamic dispersion relations.

Findings

Polarization reduces effective viscosity and extends relaxation times.

Viscosity imposes bounds on group velocity and links polarization to relaxation times.

Results impact understanding of low viscosity and shear-vorticity coupling in strongly interacting matter.

Abstract

We perform a causality analysis on the dispersion relation of hydrodynamics with spin well as shear and bulk viscosity, including the relaxation times for all these quantities. We find that the interplay of the three relaxational scales, for shear and bulk viscosity as well as polarization, leads to non-trivial effects on the dispersion relation. Unexpectedly, the presence of polarization leads to lower effective viscosity and a longer relaxation time, and the presence of viscosity leads to lower limits as well as upper ones on the group velocity and constraints relating polarization to viscosity relaxation times. We conclude with a qualitative discussion on how these results impact phenomenology, specifically the low effective viscosity in strongly interacting matter as well as shear-vorticity coupling.