Godunov Variables in Relativistic Fluid Dynamics

TL;DR

This paper introduces Godunov variables and 4-potentials for relativistic Euler equations, providing new explicit formulas and interpretations for different fluid types within the framework of symmetric hyperbolicity.

Contribution

It develops Godunov variables and 4-potentials for relativistic fluids, including explicit formulas for ideal gases, advancing the theory of convex covariant density systems.

Findings

Derived Godunov variables for relativistic fluids

Provided explicit generating function for ideal gases

Linked conservation laws to entropy and matter interpretations

Abstract

This note presents Godunov variables and 4-potentials for the relativistic Euler equations of barotropic fluids. The associated additional conservation/ production law has different interpretations for different fluids. In particular it refers to ENTROPY in the case of thermobarotropic fluids, and to MATTER in the case of isentropic fluids. The paper also presents an explicit formula for the generating function of the Euler equations in the case of ideal gases. It pursues ideas on symmetric hyperbolicity going back to Godunov (cf. also Lax and Friedrichs as well as Boillat) that were elaborated as Ruggeri and Strumia's theory of convex covariant density systems.