Anisotropic expansion, dissipative hydrodynamics from kinetic theory

TL;DR

This paper derives dissipative hydrodynamic equations for anisotropic expanding fluids using kinetic theory, specifically the relativistic Boltzmann equation, extending previous models to Kasner space-time.

Contribution

It introduces a novel derivation of second and third order evolution equations for anisotropic expansion from kinetic theory, generalizing existing models.

Findings

Equations reduce to 1D expansion case under certain conditions.

Derived evolution equations for shear stress tensor and energy density.

Validated the consistency with known isotropic and anisotropic expansion models.

Abstract

We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second and third order evolution equations reduce to those of one dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.