# Anisotropic fluid dynamics for Gubser flow

## TL;DR

This paper evaluates various hydrodynamic models for Gubser flow, finding anisotropic hydrodynamics most accurately reproduces the microscopic kinetic evolution by matching pressure anisotropies, and discusses optimal modeling strategies.

## Contribution

It demonstrates that anisotropic hydrodynamics best approximates the exact kinetic evolution in Gubser flow and provides insights into optimal matching procedures for anisotropic hydrodynamic frameworks.

## Key findings

- Anisotropic hydrodynamics closely matches the exact kinetic evolution.
- Adding residual shear stress improves non-optimized matching.
- Insights are provided for modeling strongly-coupled systems without kinetic descriptions.

## Abstract

Exploring a variety of closing schemes to the infinite hierarchy of momentum moments of the exactly solvable Boltzmann equation for systems undergoing Gubser flow, we study the precision with which the resulting hydrodynamic equations reproduce the exact evolution of hydrodynamic moments of the distribution function. We find that anisotropic hydrodynamics, obtained by ex- panding the distribution function around a dynamically evolving locally anisotropic background whose evolution is matched to exactly reproduce the macroscopic pressure anisotropy caused by the different longitudinal and transverse expansion rates in Gubser flow, provides the most accurate macroscopic description of the microscopic kinetic evolution. This confirms a similar earlier finding for Bjorken flow [Moln\'ar, Niemi and Rischke, Phys. Rev. D 94, 125003 (2016)]. We explain the physics behind this optimal matching procedure and show that one can efficiently correct for a non- optimized matching choice by adding a residual shear stress to the energy-momentum tensor whose evolution is again determined by the Boltzmann equation. Additional insights to guide the optimal choice of a macroscopic anisotropic hydrodynamic framework for strongly-coupled systems that do not admit a microscopic kinetic description are reported.