Variational principle of relativistic perfect fluid

TL;DR

This paper reformulates the relativistic perfect fluid equations on curved space-time using a variational principle, deriving covariant Euler-Lagrange equations that yield the fundamental fluid dynamics equations in a reparametrization invariant form.

Contribution

It introduces a variational formulation for relativistic perfect fluids on curved space-time, providing a covariant derivation of the Euler and continuity equations.

Findings

Derivation of covariant Euler-Lagrange equations for relativistic fluids

Reparametrization invariant form of fluid equations

Unified variational framework for relativistic fluid dynamics

Abstract

We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational principle. This leads to the Euler equation and the equation of continuity in reparametrization invariant form.