Plane waves in noncommutative fluids

TL;DR

This paper investigates the behavior of noncommutative fluids in Snyder space, deriving linearized equations and identifying plane wave solutions, thereby advancing understanding of noncommutative fluid dynamics.

Contribution

It introduces a perturbative approach to noncommutative fluid dynamics in Snyder space and finds explicit plane wave solutions, a novel contribution to the field.

Findings

Plane wave solutions for fluid density and potentials identified

Energy-momentum tensor for plane waves calculated

Linearized equations describe noncommutative fluid behavior

Abstract

We study the dynamics of the noncommutative fuid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monocromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated.