Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

TL;DR

This paper introduces a new exact solution to the Boltzmann equation for a system with specific symmetries, enabling validation of relativistic hydrodynamics models across different viscosity regimes.

Contribution

The authors derive a novel exact solution to the Boltzmann equation using conformal mapping, applicable to systems with boost-invariance and symmetry, facilitating direct comparison with hydrodynamic approximations.

Findings

Exact kinetic solution matches hydrodynamic models in ideal and viscous regimes.

Provides a benchmark for testing relativistic hydrodynamics validity.

Enhances understanding of the transition between kinetic theory and hydrodynamics.

Abstract

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.