Linear stability of Israel-Stewart theory in the presence of net-charge diffusion

TL;DR

This paper analyzes the linear stability of Israel-Stewart theory considering shear stress, net-baryon diffusion, and their coupling, deriving conditions for stability and constraints on transport coefficients.

Contribution

It provides a comprehensive stability analysis of Israel-Stewart theory with diffusion effects, establishing new constraints on relaxation times and transport coefficients.

Findings

Identified all relevant modes of the theory.

Derived necessary conditions for stability and subluminality.

Established constraints on relaxation times and diffusion-viscous coupling coefficients.

Abstract

In this paper, we perform a linear stability analysis of Israel-Stewart theory around a global equilibrium state, including the effects of shear-stress tensor, net-baryon diffusion current and diffusion-viscous coupling. We find all the relevant modes of this theory and derive necessary conditions that these modes must satisfy in order to be stable and subluminal. With these conditions, we then derive constraints for the shear and diffusion relaxation times and the transport coefficients related to diffusion-viscous coupling.