Analytical structure of the binary collision integral and the ultrarelativistic limit of transport coefficients of an ideal gas

TL;DR

This paper analytically investigates the binary collision integral for ultrarelativistic gases, deriving transport coefficients and their mass corrections, advancing the theoretical understanding of relativistic fluid dynamics.

Contribution

It provides an analytical framework for the collision integral and computes transport coefficients, including mass corrections, for ultrarelativistic ideal gases.

Findings

Analytical expressions for linearized collision matrices.

Numerical computation of second-order transport coefficients.

Exact leading-order mass corrections to bulk viscosity and relaxation times.

Abstract

In this paper we discuss the analytical properties of the binary collision integral for a gas of ultrarelativistic particles interacting via a constant cross-section. Starting from a near-equilibrium expansion over a complete basis of irreducible tensors in momentum space we compute the linearized collision matrices analytically. Using these results we then numerically compute all transport-coefficients of relativistic fluid dynamics with various power-counting schemes that are second-order in Knudsen and/or inverse Reynolds numbers. Furthermore, we also exactly compute the leading-order contribution with respect to the particle mass to the coefficient of bulk viscosity, the relaxation time, and other second-order transport coefficients of the bulk viscous pressure.