Formulating Viscous Hydrodynamics for Large Velocity Gradients

TL;DR

This paper extends viscous hydrodynamics formulations to large velocity gradients using Israel-Stewart equations, analyzing parameters for stability, physicality, and potential constraints from lattice calculations.

Contribution

It relates Israel-Stewart parameters to fluctuations and entropy constraints, and explores their role in stable, physical solutions and lattice-based parameter constraints.

Findings

Israel-Stewart parameters linked to tau_ij fluctuations

Analysis of parameters for stable sound wave solutions

Potential for lattice calculations to constrain parameters

Abstract

Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity g radients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the s tress-energy tensor tau_ij as dynamical objects, introduce new parameters, such as the relaxati on times describing non-equilibrium behavior of the elements tau_ij. By considering linear resp onse theory and entropy constraints, we show how the additional parameters are related to fluctuatio ns of tau_ij. Furthermore, the Israel-Stewart parameters are analyzed for their ability to prov ide stable and physical solutions for sound waves. Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calcu lations, which are based on path-integral formulations in imaginary time.