Analytical formulas for shear and bulk viscosities in relativistic gaseous mixtures with constant cross sections

• Analytical formulas for the shear and the bulk viscosities in mixtures are derived.
• First principles based calculations.
• Additional expressions for auxiliary quantities are presented.
• Single-component shear viscosity is corrected.
• Some analysis and convenient methodology are presented.

Using Mathematica package, we derive analytical closed-form expressions for the shear and the bulk viscosity coefficients in multicomponent relativistic gases with constant cross sections, being the relativistic generalization for the hard spheres model. Some of them are cumbersome and require symbolic manipulations in an algebraic package. The constant cross sections are of the elastic processes, while the inelastic (or number-changing) processes (collisions or decays) are considered only partly. As examples, we find explicit expressions of the correct single-component first-order shear viscosity coefficient and some explicit analytical results for the binary mixture. These formulas have numerous applications in approximate nonequilibrium descriptions of gases of particles or quasiparticles with averaged (temperature dependent) cross sections. In addition to this, we present formulas for collision rates and some other related formulas.