The Relaxation Effect in Dissipative Relativistic Fluid Theories

TL;DR

This paper investigates how causal dissipative relativistic fluid theories predict that fluid states relax over microscopic timescales to resemble the simpler relativistic Navier-Stokes models with minor dissipative effects.

Contribution

It demonstrates that physical states in these theories naturally relax to forms similar to relativistic Navier-Stokes solutions, clarifying the behavior of dissipative relativistic fluids.

Findings

Fluid states relax to Navier-Stokes-like forms within microscopic timescales.

Relaxed states are indistinguishable from perfect fluids with small dissipative corrections.

The relaxation process is characterized by microscopic interaction times.

Abstract

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple relativistic Navier-Stokes descriptions of these states. Thus, for example, in the relaxed form of a physical fluid state the stress energy tensor is in effect indistinguishable from a perfect fluid stress tensor plus small dissipative corrections proportional to the shear of the fluid velocity, the gradient of the temperature, etc.