Analytic solutions of the relativistic Boltzmann equation

TL;DR

This paper derives new analytic solutions to the relativistic Boltzmann equation, enabling comparison with hydrodynamic models and revealing novel boost-invariant behaviors relevant to high-energy physics.

Contribution

It introduces spherically expanding and boost-invariant analytic solutions to the relativistic Boltzmann equation, connecting kinetic theory with hydrodynamics and fluid-gravity correspondence.

Findings

Spherically expanding solutions match Israel-Stewart equations

Discovery of a novel boost-invariant solution with unconventional proper time dependence

Analytical comparison between kinetic and hydrodynamic solutions

Abstract

We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second order hydrodynamics and fluid-gravity correspondence.