Flux-variational formulation of relativistic perfect fluids

TL;DR

This paper presents a new variational formulation for relativistic perfect fluids on pseudoriemannian manifolds, deriving Euler and continuity equations without constraints.

Contribution

It introduces a flux-variational approach that simplifies deriving fluid equations in a relativistic geometric setting.

Findings

Euler and continuity equations derived directly

No constraints needed in the variational formulation

Applicable to general pseudoriemannian manifolds

Abstract

We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity equations are obtained quite directly.