Gradient expansion for anisotropic hydrodynamics

TL;DR

This paper computes the gradient expansion for anisotropic hydrodynamics, compares it with kinetic theory, and finds that a recent formulation aligns well with kinetic results, supporting its validity as an approximation.

Contribution

It demonstrates that a recent anisotropic hydrodynamics formulation accurately reproduces the first three gradient expansion terms of kinetic theory, validating its effectiveness.

Findings

First three gradient terms match kinetic theory

Gradient expansion is asymptotic

Non-hydrodynamic modes indicated by Borel analysis

Abstract

We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes.