Streamlines of perfect fluid as geodesics in Riemannian space-time

TL;DR

This paper shows that streamlines of a relativistic perfect isentropic fluid are geodesics in a Riemannian space defined by the fluid's enthalpy, simplifying problem-solving and offering insights into fundamental physics.

Contribution

It establishes that fluid streamlines correspond to geodesics in a Riemannian space with a metric based on enthalpy, providing a novel geometric perspective.

Findings

Streamlines are geodesics in a Riemannian space.

The metric is defined by the fluid's enthalpy.

This approach simplifies certain fluid dynamics problems.

Abstract

Streamlines of a relativistic perfect isentropic fluid are geodesics of a Riemannian space whose metric is defined by enthalpy of the fluid. This fact simplifies the solution of some problems, as is also of interest from the point of view of fundamental physics.