Noncommutative Geometry and Fluid Dynamics

TL;DR

This paper develops a noncommutative generalization of perfect fluid dynamics within a Hamiltonian framework, deriving new algebraic structures and applying them to extend cosmological models with anisotropy and inhomogeneity.

Contribution

It introduces a novel noncommutative fluid model from first principles and applies it to extend the FRW cosmological model with NC effects.

Findings

Derived NC fluid bracket algebra and conservation laws.

Identified NC correction terms in charge and energy fluxes.

Extended Friedmann equation incorporating NC effects.

Abstract

In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing in anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation.