# Viscous anisotropic hydrodynamics for the Gubser flow

## TL;DR

This paper develops and tests a viscous anisotropic hydrodynamics model for Gubser flow, deriving equations from an advanced moments method, and demonstrates its superior accuracy compared to other hydrodynamic models.

## Contribution

It introduces a novel anisotropic hydrodynamics framework based on the moments method for Gubser flow, with equations that match an exact solution more closely than existing models.

## Key findings

- The derived equations accurately reproduce the exact Gubser flow solution.
- The MNR anisotropic hydrodynamics outperforms other hydrodynamical approaches.
- Numerical solutions show improved agreement with the exact relaxation-time Boltzmann solution.

## Abstract

In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Moln\'ar et al. (MNR) [1,2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the $SO(3)_q\otimes SO(1,1)\otimes Z_2$ symmetry of the Gubser flow in the deSitter space. These equations are solved numerically and compared with the predictions of the recently found exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We also compare our numerical results with other fluid dynamical models. We observe that the MNR description of anisotropic fluid dynamics reproduces the space-time evolution of the system than all other currently known hydrodynamical approaches.