Causality and stability analysis for the minimal causal spin hydrodynamics

TL;DR

This paper analyzes the causality and stability of minimal spin hydrodynamics up to second order, revealing conditions for stability and causality, and highlighting differences from conventional hydrodynamics.

Contribution

It introduces a second-order minimal causal spin hydrodynamics framework and derives new causality and stability conditions, emphasizing the role of spin density and chemical potentials.

Findings

First-order spin hydrodynamics is acausal and unstable.

Second-order minimal causal spin hydrodynamics can be stable under certain conditions.

Stability depends on the equations of state and wave-vector regimes.

Abstract

We perform the linear analysis of causality and stability for a minimal extended spin hydrodynamics up to second order of the gradient expansion. The first order spin hydrodynamics, with a rank-3 spin tensor being antisymmetric for only the last two indices, are proved to be acausal and unstable. We then consider the minimal causal spin hydrodynamics up to second order of the gradient expansion. We derive the necessary causality and stability conditions for this minimal causal spin hydrodynamics. Interestingly, the satisfaction of the stability conditions relies on the equations of state for the spin density and chemical potentials. Moreover, different with the conventional relativistic dissipative hydrodynamics, the stability of the theory seems to be broken at the finite wave-vector when the stability conditions are fulfilled at small and large wave-vector limits. It implies that the behavior in small and large wave-vector limits may be insufficient to determine the stability conditions for spin hydrodynamics in linear mode analysis.