Out-of-equilibrium Gubser flow attractors

TL;DR

This paper investigates the non-equilibrium attractors in Gubser flow using kinetic theory and compares various hydrodynamic models, finding anisotropic hydrodynamics best matches the exact Boltzmann solution.

Contribution

It identifies the attractors of different hydrodynamic theories in Gubser flow and demonstrates anisotropic hydrodynamics' superior accuracy in reproducing the exact solution.

Findings

Anisotropic hydrodynamics closely matches the exact Boltzmann attractor.

Other hydrodynamic models fail to accurately reproduce the attractor.

The basin of attraction is three-dimensional and non-planar.

Abstract

We discuss the non-equilibrium attractors of systems undergoing Gubser flow within kinetic theory by means of nonlinear dynamical systems. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories. These attractors are non-planar and the basin of attraction is three dimensional. We compare the asymptotic attractors of each hydrodynamic model with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. Anisotropic hydrodynamics matches, up to high numerical accuracy, the attractor of the exact theory while the other hydrodynamic theories fail to do so. Thus, anisotropic hydrodynamics is an effective theory for far-from-equilibrium fluids, which consists of the dissipative (nonperturbative) contributions at any order in the gradient expansion.