Anisotropic hydrodynamics for conformal Gubser flow

TL;DR

This paper derives an exact solution for anisotropic hydrodynamics under Gubser flow, demonstrating improved accuracy over existing dissipative hydrodynamics methods by solving coupled differential equations and comparing with Boltzmann equation solutions.

Contribution

It provides the first exact solution of anisotropic hydrodynamics equations for Gubser flow, reducing the problem to two coupled equations and validating the approach against Boltzmann equation results.

Findings

Anisotropic hydrodynamics better describes system evolution than other dissipative approaches.

The solution reduces to ideal or free streaming limits under specific relaxation times.

Numerical solutions agree well with Boltzmann equation benchmarks.

Abstract

In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3)_q symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubser's ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.