Kinetic theory and the speed of sound in dense matter

TL;DR

This paper explores a constraint on the speed of sound in dense matter derived from relativistic kinetic theory, linking instantaneous and average sound speeds to better understand the equation of state's stiffness.

Contribution

It introduces a reformulation of the kinetic-theory bound in terms of average and instantaneous sound speeds, providing a new visualization method.

Findings

Derived a relation between $c_s^2$ and $ angle c_s^2 angle$

Visualized the kinetic-theory bound in the $c_s^2$-$ angle c_s^2 angle$ plane

Enhanced understanding of the stiffness constraints of dense matter

Abstract

We discuss a constraint on the speed of sound, $c_s^2$, derived from relativistic kinetic theory and show how it can be expressed in terms of the average sound speed, $\langle c_s^2 \rangle$. This reformulation highlights the interplay between instantaneous and integrated stiffness of the equation of state and allows the kinetic-theory bound to be visualized as a restriction in the $c_s^2$-$\langle c_s^2 \rangle $ plane.