Extending Israel-Stewart theory: Causal bulk viscosity at large gradients

TL;DR

This paper develops extended relativistic fluid models with bulk viscosity that remain causal and well-behaved even far from equilibrium, improving upon Israel-Stewart theory for large viscous stresses.

Contribution

The authors introduce a class of models that extend Israel-Stewart theory, ensuring causality and hyperbolicity at large viscous stresses and far-from-equilibrium conditions.

Findings

Models remain symmetric hyperbolic and causal at all times.

The second law of thermodynamics is exactly enforced.

Models accommodate complex dependencies of bulk viscosity on density and temperature.

Abstract

We present a class of relativistic fluid models for cold and dense matter with bulk viscosity, whose equilibrium equation of state is polytropic. These models reduce to Israel-Stewart theory for small values of the viscous stress $\Pi$. However, when $\Pi$ becomes comparable to the equilibrium pressure $P$, the evolution equations "adjust" to prevent the onset of far-from-equilibrium pathologies that would otherwise plague Israel-Stewart. Specifically, the equations of motion remain symmetric hyperbolic and causal at all times along any continuously differentiable flow, and across the whole thermodynamic state space. This means that, no matter how fast the fluid expands or contracts, the hydrodynamic equations are always well-behaved (away from singularities). The second law of thermodynamics is enforced exactly. Near equilibrium, these models can accommodate an arbitrarily complicated dependence of the bulk viscosity coefficient $\zeta$ on both density and temperature.