Hydrodynamic Flow as Congruence of Geodesic Lines in Riemannian Space-Time

TL;DR

This paper demonstrates that small elements of perfect fluid undergoing adiabatic processes follow geodesic lines in a Riemannian space-time, linking fluid dynamics with geometric properties of space-time.

Contribution

It establishes a geometric interpretation of perfect fluid motion in Riemannian space-time, connecting hydrodynamics with differential geometry.

Findings

Perfect fluid elements move along geodesics in Riemannian space-time.

Adiabatic processes preserve the geodesic motion of fluid elements.

Provides a geometric framework for understanding fluid dynamics in curved space-time.

Abstract

It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.