Steady asymptotic equilibria in conformal relativistic fluids

TL;DR

This paper derives an exact decay rate to equilibrium for conformal fluids in kinetic theory, compares it with hydrodynamic models, and shows improvements with higher-moment schemes.

Contribution

It provides an exact solution for decay rates in conformal fluids and compares different hydrodynamic approximations, highlighting the benefits of including higher moments.

Findings

Second-moment hydrodynamics improves decay rate predictions

Exact kinetic theory solution matches well with extended hydrodynamic models

Higher moments lead to better approximation of relaxation dynamics

Abstract

When one considers a shock wave in the frame where the shock is at rest, on either side one has a steady flow which converges to equilibrium away from the shock. However, hydrodynamics is unable to describe this flow if the asymptotic velocity is higher than the characteristic speed of the theory. We obtain an exact solution for the decay rate to equilibrium for a conformal fluid in kinetic theory under the relaxation time approximation, and compare it to two hydrodynamic schemes, one accounting for the second moments of the distribution function and thus equivalent, in the small deviations from equilibrium limit, to an Israel-Stewart framework, and another accounting for both second and third moments. While still having a finite characteristic speed, the second model is a significant improvement on the first.