# Exact solutions of the relativistic Boltzmann equation in the relaxation time approximation

## TL;DR

This paper derives exact solutions to the relativistic Boltzmann equation under the relaxation time approximation for a mixture of massless bosons and massive fermions in a one-dimensional, boost-invariant expansion, extending previous single-component results.

## Contribution

It provides the first exact solutions for coupled RTA kinetic equations for bosons and fermions, generalizing earlier single-component and classical particle results.

## Key findings

- Exact solutions for coupled boson-fermion systems in RTA
- Generalization of previous single-component results
- Analytic and numerical methods used for solution

## Abstract

This Thesis concentrates on the analysis of coupled RTA (relaxation time approximation) kinetic equations for bosons and fermions. Bosons are treated as massless particles, while fermions have a finite mass. Using analytic and numerical methods we find exact solutions for such a mixture in the case of one-dimensional, boost-invariant expansion (for systems which are transversally homogeneous). In this way, several earlier results obtained for one-component systems and classical particles are generalized.