The causality and stability of relativistic spin-hydrodynamics

TL;DR

This paper investigates the causality and stability of relativistic spin-hydrodynamics, revealing that first-order models are unstable and acausal, and highlighting the need for a causal, stable theory incorporating spin effects.

Contribution

It introduces and analyzes two models of relativistic spin-hydrodynamics, demonstrating their instabilities and acausal behaviors, and emphasizes the necessity for a consistent causal framework.

Findings

First-order dissipative spin-hydrodynamics is acausal and unstable.

New linear modes emerge due to spin, exhibiting instability and acausality.

Second-order model supports sound waves but can be unstable with vorticity.

Abstract

We study the causality and stability of relativistic hydrodynamics with the inclusion of the spin degree of freedom as a hydrodynamic field. We consider two specific models of spin-hydrodynamics for this purpose. A linear mode analysis for static background shows that a first-order dissipative spin-hydrodynamics remains acausal and admits instabilities. Besides, it is found that the inclusion of the spin field in hydrodynamics leads to new kinds of linear modes in the system. These new modes also exhibit instability and acausal behavior. The second model of the spin-hydrodynamics that we have considered here is equivalent to a particular second-order conventional hydrodynamics with no dissipative effects. For a static background, it is found that the linear modes of this model support the sound waves only. However, when the background has constant vorticity, then the model admits instability and acausality in certain situations. It is found that the spin-dynamics have an effect on the hydrodynamic response of the fluid. These findings point toward the need for a causal and stable theory with spin as a hydrodynamic field to describe the spin-polarized fluid.