Covariant Fluid Dynamics: a Long Wave-Length Approximation

TL;DR

This paper analyzes the Long-Wavelength Approximation Scheme within covariant fluid dynamics in general relativity, focusing on irrotational dust models near singularities, and confirms that magnetic Weyl tensor effects lead to bounces between Kasner phases.

Contribution

It provides an analytic study of LWAS in covariant fluid models, highlighting the role of magnetic Weyl tensor in singularity behavior, extending previous numerical findings.

Findings

Magnetic Weyl tensor causes bounces between Kasner phases.

Expanding regions evolve as separate universes with diminishing inhomogeneities.

Analytic results confirm previous numerical analyses.

Abstract

In this paper we consider the Long-Wavelength Approximation Scheme (LWAS) in the framework of the covariant fluid approach to general relativistic dynamics, specializing to the particular case of irrotational dust matter. We discuss the dynamics of these models during the approach to any spacelike singularity where a BKL-type evolution is expected, studying the validity of this approximation scheme and the role of the magnetic part of the Weyl tensor, $H_{ab}$. Our analytic results confirm a previous numerical analysis: it is $H_{ab}$ that destroys the pure Kasner-like approach to the singularity and eventually produces the bounce to another Kasner phase. Expanding regions evolve as separate universes where inhomogeneities and anisotropies die away.