Friedmann limits of rotating hypersurface-homogeneous dust models

TL;DR

This paper systematically investigates the conditions under which rotating hypersurface-homogeneous dust models can approach Friedmann models, including transitions involving changes in Bianchi types, and explicitly calculates various limiting cases.

Contribution

It provides a comprehensive analysis of Friedmann limits for all rotating hypersurface-homogeneous dust models, including transitions between different Bianchi types and explicit calculations of key limits.

Findings

Friedmann limits exist for all non-stationary rotating models.

Each Friedmann model has specific parent classes within the rotating models.

Explicit limits for zero rotation, tilt, shear, and isotropy are derived.

Abstract

The existence of Friedmann limits is systematically investigated for all the hypersurface-homogeneous rotating dust models, presented in previous papers by this author. Limiting transitions that involve a change of the Bianchi type are included. Except for stationary models that obviously do not allow it, the Friedmann limit expected for a given Bianchi type exists in all cases. Each of the 3 Friedmann models has parents in the rotating class; the k = +1 model has just one parent class, the other two each have several parent classes. The type IX class is the one investigated in 1951 by Goedel. For each model, the consecutive limits of zero rotation, zero tilt, zero shear and spatial isotropy are explicitly calculated.