Thermal Conductivity, Shear and Bulk Viscosities for a Relativistic Binary Mixture

TL;DR

This paper derives analytical expressions for thermal conductivity, shear, and bulk viscosities of a relativistic binary gas mixture under gravitational influence using kinetic theory and the Boltzmann equation.

Contribution

It provides new formulas for transport coefficients in relativistic binary mixtures considering gravitational effects and particle interactions.

Findings

Transport coefficients depend on relativistic parameter and gravitational potential.

Analytical expressions are derived for thermal conductivity, shear, and bulk viscosities.

Transport coefficients vary with the relativistic regime and gravitational influence.

Abstract

In the present work, we deal with a binary mixture of diluted relativistic gases within the framework of the kinetic theory. The analysis is made within the framework of the Boltzmann equation. We assume that the gas is under the influence of an isotropic Schwarzschild metric and is composed of particles with speeds comparable with the light speed. Taking into account the constitutive equations for the laws of Fourier and Navier-Stokes, we obtain expressions for the thermal conductivity, the shear, and bulk viscosities. To evaluate the integrals we assume a hard-sphere interaction along with non-disparate masses for the particles of each component. We show the analytical expressions and the behavior of the transport coeffcients with respect to a relativistic parameter which gives the ratio of the rest energy of the particles to the thermal energy of the gas.We also determine the dependence of the transport coeffcients with respect to the gravitational potential and demonstrate that the corresponding one component