On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

TL;DR

This paper proves that the relativistic Euler system with a kinetic equation of state is hyperbolic and respects causality, confirming conjectures about the existence of normal solutions to the relativistic Boltzmann equation across all positive temperatures.

Contribution

It validates conjectures ensuring the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state for all positive temperatures.

Findings

Relativistic Euler system is hyperbolic.

Speed of sound is bounded by c/√3.

Conjectures about normal solutions are confirmed.

Abstract

We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that the relativistic Euler system under the kinetic equation of state is hyperbolic and the speed of sound cannot overcome $c/\sqrt{3}$.