Divergence of the Chapman-Enskog expansion in relativistic kinetic theory

TL;DR

This paper demonstrates that the relativistic Chapman-Enskog expansion diverges for a massless gas undergoing Bjorken expansion and introduces a new non-perturbative expansion method that aligns well with exact solutions.

Contribution

It presents the first evidence of divergence in the relativistic Chapman-Enskog series and proposes a novel non-perturbative expansion approach to address this issue.

Findings

Chapman-Enskog series diverges for massless gases in Bjorken expansion

Proposed expansion includes non-perturbative contributions in the Knudsen number

New method agrees well with exact Boltzmann solutions across various Knudsen numbers

Abstract

In this letter we show for the first time that the relativistic Chapman-Enskog series for a massless gas undergoing Bjorken expansion diverges. In order to fix this problem, we propose a novel type of expansion that includes non-perturbative contributions in the Knudsen number that are not considered in Chapman-Enskog theory. This approach is in good agreement with exact solutions of the Boltzmann equation for a wide range of values of Knudsen number and does not display the clear signs of divergence exhibited by the Chapman-Enskog series.