The Covariant Approach to LRS Perfect Fluid Spacetime Geometries

TL;DR

This paper reformulates the dynamics of LRS perfect fluid spacetimes using a covariant 1+3 threading approach, simplifying the equations to scalar relations and exploring models with higher symmetries.

Contribution

It introduces a covariant 1+3 threading formalism for LRS perfect fluid spacetimes, offering an alternative to the orthonormal frame method and analyzing symmetric subcases.

Findings

Reduced dynamical equations to scalar differential relations.

Clarified consistency conditions for LRS models.

Explored higher symmetry models within LRS class.

Abstract

The dynamics of perfect fluid spacetime geometries which exhibit {\em Local Rotational Symmetry} (LRS) are reformulated in the language of a $1+\,3$ "threading" decomposition of the spacetime manifold, where covariant fluid and curvature variables are used. This approach presents a neat alternative to the orthonormal frame formalism. The dynamical equations reduce to a set of differential relations between purely scalar quantities. The consistency conditions are worked out in a transparent way. We discuss their various subcases in detail and focus in particular on models with higher symmetries within the class of expanding spatially inhomogeneous LRS models, via a consideration of functional dependencies between the dynamical variables.