Hydrodynamics of an ultra-relativistic fluid in the flat anisotropic cosmological model

TL;DR

This paper investigates the behavior of an ultra-relativistic perfect fluid in anisotropic cosmological models, revealing tendencies toward inhomogeneity formation and analyzing vortex dynamics under non-stationary anisotropic conditions.

Contribution

It introduces a Hamiltonian approach to relativistic fluid dynamics in Kasner spacetime and explores the effects of anisotropy on sound waves and vortex behavior.

Findings

Formation of strong inhomogeneities at small times

Hydrodynamics of slow vortices matches Eulerian incompressible flow with external strain

Anisotropy influences sound wave propagation and vortex dynamics

Abstract

Motion of an ultra-relativistic perfect fluid in space-time with the Kasner metrics is investigated by the Hamiltonian method. It is found that in the limit of small times a tendency takes place to formation of strong inhomogeneities in matter distribution. In the case of slow flows the effect of non-stationary anisotropy on dynamics of sound waves and behaviour of frozen-in vortices is considered. It is shown that hydrodynamics of slow vortices on the static homogeneous background is equivalent to the usual Eulerian incompressible hydrodynamics, but in the presence of an external non-stationary strain velocity field.