Characterisation of orthogonal perfect fluid cosmological spacetimes

TL;DR

This paper characterizes orthogonal perfect fluid cosmological spacetimes, showing that homogeneous models are limited to FLRW or Bianchi I, while inhomogeneous models admit specific symmetries and singularity properties.

Contribution

It provides a classification of orthogonal perfect fluid spacetimes based on symmetry and singularity features, highlighting the uniqueness of the non-singular cylindrically symmetric family.

Findings

Homogeneous models are only FLRW or Bianchi I.

Inhomogeneous models admit G_2 isometry groups.

A unique non-singular cylindrically symmetric family exists.

Abstract

We consider the general orthogonal metric separable in space and time variables in comoving coordinates. We then characterise perfect fluid models admitted by such a metric. It turns out that the homogeneous models can only be either FLRW or Bianchi I while the inhomogeneous ones can only admit $G_2 $ (two mutually as well as hypersurface orthogonal spacelike Killing vectors) isometry. The latter can possess singularities of various kinds or none. The non-singular family is however unique and cylindrically symmetric.