Non-metric fluid dynamics and cosmology on Finsler spacetimes

TL;DR

This paper extends fluid dynamics to Finsler spacetimes, showing that collisionless fluids follow Liouville equations and deriving generalized Euler equations for dust in cosmological models.

Contribution

It introduces a generalized kinetic theory of fluids on Finsler geometries, expanding the framework beyond metric spacetimes.

Findings

Finsler spacetimes support fluid dynamics similar to metric backgrounds.

Collisionless fluids obey Liouville equations in Finsler geometry.

Derived generalized Euler equations for dust fluids with cosmological symmetry.

Abstract

We generalize the kinetic theory of fluids, in which the description of fluids is based on the geodesic motion of particles, to spacetimes modeled by Finsler geometry. Our results show that Finsler spacetimes are a suitable background for fluid dynamics and that the equation of motion for a collisionless fluid is given by the Liouville equation, as it is also the case for a metric background geometry. We finally apply this model to collisionless dust and a general fluid with cosmological symmetry and derive the corresponding equations of motion. It turns out that the equation of motion for a dust fluid is a simple generalization of the well-known Euler equations.