Noncommutative Geometry and Fluid Dynamics

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.

15 pages, no figures, change of title, new references added, no change in results and conclusions; minor changes and references added, to appear in EPJC; erratum included (page 19), change in Dirac algebra leads to significant changes in some of the conclusions

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Cited by in corpus (11)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Stochastic motion in an expanding noncommutative fluid
• Noncommutative fluid and Growing Modes of Inhomogeneity in (Newtonian) Cosmology
• Back Reaction Inhomogeneities in Cosmological Parameter Evolution via Noncommutative Fluid
• Influences of the coordinate dependent noncommutative space on charged and spin currents
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation
• Simulating Non Commutative Geometry with Quantum Walks
• Non-Commutative fluid: an alternative source of cosmic acceleration