Nonlinear Constraints on Relativistic Fluids Far From Equilibrium

TL;DR

This paper derives fundamental nonlinear constraints ensuring causality, local existence, and uniqueness in Israel-Stewart-like relativistic fluid theories far from equilibrium, accounting for viscosities without simplifying assumptions.

Contribution

It introduces new nonlinear causality constraints for relativistic viscous fluids far from equilibrium, extending previous linear or near-equilibrium analyses.

Findings

Identifies necessary causality conditions for nonlinear relativistic fluids.

Provides sufficient conditions for local existence and uniqueness of solutions.

Establishes bounds on viscous corrections in far-from-equilibrium regimes.

Abstract

New constraints are found that must necessarily hold for Israel-Stewart-like theories of fluid dynamics to be causal far away from equilibrium. Conditions that are sufficient to ensure causality, local existence, and uniqueness of solutions in these theories are also presented. Our results hold in the full nonlinear regime, taking into account bulk and shear viscosities (at zero chemical potential), without any simplifying symmetry or near-equilibrium assumptions. Our findings provide fundamental constraints on the magnitude of viscous corrections in fluid dynamics far from equilibrium.