Perfect spinfluid: A divergence-type approach

TL;DR

This paper introduces a divergence-type formulation of relativistic spin hydrodynamics that guarantees causality, stability, and well-posedness, enabling accurate simulations of spin-polarized fluids like quark-gluon plasma.

Contribution

It develops a new divergence-type framework for non-dissipative relativistic spin hydrodynamics, ensuring causality and stability to all orders in spin potential.

Findings

The equations are non-linearly causal and symmetric-hyperbolic under specific conditions.

The framework applies to numerical simulations of spin-polarized fluids.

Proven stability and causality in a spin kinetic theory realization.

Abstract

We present a new formulation of non-dissipative relativistic spin hydrodynamics that incorporates spin degrees of freedom into the divergence-type theory framework. Due to the divergence-type structure, it is straightforward to enforce non-linear causality and symmetric hyperbolicity of the equations of motion, ensuring local well-posedness of the initial-value problem and stability of the theory. Furthermore, in a specific realization based on spin kinetic theory, we prove that the equations of motion remain non-linearly causal and symmetric-hyperbolic to all orders in the spin potential, provided a specific thermodynamic constraint is satisfied. This framework can be applied for numerical simulations to study the dynamics of spin-polarized fluids, such as the quark-gluon plasma in heavy-ion collisions.