Causal third-order viscous hydrodynamics within relaxation-time approximation

Abstract

In the present work, we derive a linearly stable and causal theory of relativistic third-order viscous hydrodynamics from the Boltzmann equation with relaxation-time approximation. We employ viscous correction to the distribution function obtained using a Chapman-Enskog like iterative solution of the Boltzmann equation. Our derivation highlights the necessity of incorporating a new dynamical degree of freedom, specifically an irreducible tensors of rank three, within this framework. This differs from the recent formulation of causal third-order theory from the method of moments which requires two dynamical degrees of freedom: an irreducible third-rank and a fourth-rank tensor. We verify the linear stability and causality of the proposed formulation by examining perturbations around a global equilibrium state.