The matter Lagrangian of an ideal fluid

TL;DR

This paper demonstrates that the matter Lagrangian for an ideal fluid is equivalent to its total energy density, including rest and internal energies, with sign conventions depending on definitions and metric signature.

Contribution

It clarifies the precise form of the matter Lagrangian for an ideal fluid, linking it directly to the total energy density.

Findings

Matter Lagrangian equals total energy density of the fluid.

Sign conventions depend on definitions and metric signature.

Provides a clearer understanding of fluid dynamics in relativistic theories.

Abstract

We show that the matter Lagrangian of an ideal fluid equals (up to a sign -depending on its definition and on the chosen signature of the metric) the total energy density of the fluid, i.e. rest energy density plus internal energy density.