Transport coefficients for bulk viscous evolution in the relaxation time approximation

TL;DR

This paper derives new transport coefficients for bulk viscous evolution in relativistic hydrodynamics using the Chapman-Enskog method, showing improved agreement with exact solutions over previous approximations.

Contribution

It introduces a Chapman-Enskog based calculation of transport coefficients, differing from the 14-moment approximation, and demonstrates their improved accuracy in modeling viscous evolution.

Findings

Chapman-Enskog transport coefficients differ from 14-moment results for finite particle mass.

Chapman-Enskog coefficients better match exact Boltzmann solutions in boost-invariant expansion.

Bulk viscous pressure evolution is significantly influenced by shear stress coupling.

Abstract

We derive the form of the viscous corrections to the phase-space distribution function due to the bulk viscous pressure and shear stress tensor using the iterative Chapman-Enskog method. We then calculate the transport coefficients necessary for the second-order hydrodynamic evolution of the bulk viscous pressure and the shear stress tensor. We demonstrate that the transport coefficients obtained using the Chapman-Enskog method are different than those obtained previously using the 14-moment approximation for a finite particle mass. Specializing to the case of boost-invariant and transversally homogeneous longitudinal expansion, we show that the transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation in the relaxation-time approximation compared to results obtained in the 14-moment approximation. Finally, we explicitly confirm that the time evolution of the bulk viscous pressure is significantly affected by its coupling to the shear stress tensor.