Kinematic and Weyl singularities

TL;DR

This paper investigates the nature of singularities in Bianchi cosmologies, focusing on Weyl and kinematic singularities, and introduces methods to predict their occurrence based on Weyl parameters and observer behavior.

Contribution

It derives boost formulas for the Weyl tensor in tilted Bianchi models and classifies singularities as Weyl or kinematic, providing new tools for understanding cosmological singularities.

Findings

Weyl parameters tend to zero, constant, or infinity together for asymptotically null observers.

The behavior of Weyl parameters predicts the type of singularity encountered.

Kinematic variables can also indicate the presence of singularities.

Abstract

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cosmologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three classes of typical examples and one exceptional class. Given the behaviour of the Weyl parameter, we can predict that the singularity encountered is a Weyl singularity or a kinematic singularity. The analysis suggests that the kinematic variables are also useful in indicating a singularity in these models.