Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

TL;DR

This paper identifies flaws in the common relaxation time approximation for the relativistic Boltzmann equation, proposes a corrected method that preserves conservation laws, and examines its impact on transport coefficients.

Contribution

The authors introduce a new relaxation time approximation that addresses fundamental issues and maintains the properties of the linearized Boltzmann collision operator.

Findings

Corrected approximation preserves conservation laws

Significant changes in transport coefficients

Improved consistency with microscopic physics

Abstract

We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such fundamental issues and maintains the basic properties of the linearized Boltzmann collision operator. We show how this correction affects transport coefficients, such as the bulk viscosity and particle diffusion.