Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation

TL;DR

This paper derives second-order viscous hydrodynamics from kinetic theory using an extended relaxation-time approximation with energy dependence, revealing its effects on fluid evolution, isotropization, and thermalization.

Contribution

It introduces an energy-dependent relaxation time into the derivation of second-order viscous hydrodynamics from the Boltzmann equation, highlighting its impact on transport coefficients and fixed point structure.

Findings

Transport coefficients are sensitive to energy dependence.

Reproduction of stable free-streaming fixed point with power law parametrization.

Energy dependence influences isotropization and thermalization processes.

Abstract

We use the extended relaxation time approximation for the collision kernel, which incorporates a particle-energy dependent relaxation time, to derive second-order viscous hydrodynamics from the Boltzmann equation for a system of massless particles. The resulting transport coefficients are found to be sensitive to the energy dependence of the relaxation time and have significant influence on the fluid's evolution. Using the derived hydrodynamic equations, we study the evolution of a fluid undergoing (0+1)-dimensional expansion with Bjorken symmetry and investigate the fixed point structure inherent in the equations. Further, by employing a power law parametrization to describe the energy dependence of the relaxation time, we successfully reproduce the stable free-streaming fixed point for a specific power of the energy dependence. The impact of the energy-dependent relaxation time on the processes of isotropization and thermalization of an expanding plasma is discussed.