Dissipative properties of relativistic two-dimensional gases

TL;DR

This paper derives the constitutive equations for heat flux and stress tensor in a relativistic two-dimensional dilute gas, revealing unique dissipative properties and calculating transport coefficients analytically.

Contribution

It extends relativistic kinetic theory to two dimensions, deriving explicit constitutive relations and transport coefficients for a high-temperature dilute gas.

Findings

Heat flux driven by pressure and temperature gradients.

Non-zero bulk viscosity in relativistic 2D gases.

Analytical expressions for transport coefficients.

Abstract

The constitutive equations for the heat flux and the Navier tensor are established for a high temperature dilute gas in two spatial dimensions. The Chapman-Enskog procedure to first order in the gradients is applied in order to obtain the dissipative energy and momentum fluxes from the relativistic Boltzmann equation. The solution for such equation is written in terms of three sets of orthogonal polynomials which are explicitly obtained for this calculation. As in the three dimensional scenario, the heat flux is shown to be driven by the density, or pressure, gradient additionally to the usual temperature gradient given by Fourier's law. For the stress (Navier) tensor one finds, also in accordance with the three dimensional case, a non-vanishing bulk viscosity for the ideal monoatomic relativistic two-dimensional gas. All transport coefficients are calculated analytically for the case of a hard disk gas and the non-relativistic limit for the constitutive equations is verified.