The Geometrical Modelling of Fluids

TL;DR

This paper explores the connection between nonlinear electrodynamics and relativistic hydrodynamics, demonstrating how fluid fluxes can be represented as geodesics through metric transformations and conditions for converting solutions between electrodynamics types.

Contribution

It introduces a method to model fluid fluxes as geodesics via conformal metric transformations and details conditions for converting nonlinear to linear electrodynamics solutions.

Findings

Fluid fluxes can be mapped to geodesics using conformal transformations.

Conditions for transforming nonlinear to linear electrodynamics solutions are established.

The approach links electrodynamics models with relativistic hydrodynamics without dissipation.

Abstract

The paper considers the nonlinear electrodynamics type model and its relation with relativistic hydrodynamics with no dissipation (including string and membrane hydrodynamics). We are able to convert arbitrary flux of fluid to the family of geodesics by the conformal transformation of metric. The conditions of transformation of nonlinear electrodynamics solution to linear electrodynamics solution by changing of metric are presented.