Transport coefficients in second-order non-conformal viscous hydrodynamics

TL;DR

This paper evaluates the accuracy of various second-order relativistic viscous hydrodynamics models against exact solutions of the Boltzmann equation in a simplified expansion scenario, highlighting the importance of certain transport coefficients.

Contribution

It demonstrates the limitations of Israel-Stewart theory and emphasizes the significance of shear--bulk couplings in second-order hydrodynamics models.

Findings

Israel-Stewart theory fails to match exact solutions due to neglected transport coefficients.

Shear--bulk couplings are crucial for accurate bulk viscous pressure evolution.

Including coupling terms improves qualitative agreement with kinetic theory.

Abstract

Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear--bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory.