Self-similar Bianchi type VIII and IX models

TL;DR

This paper proves that certain self-similar Bianchi models cannot be tilted perfect fluids and characterizes the most general Bianchi VIII and IX spacetimes with four-dimensional homothety groups.

Contribution

It demonstrates the non-existence of self-similar Bianchi VIII and IX tilted perfect fluid models and describes the general form of Bianchi VIII and IX spacetimes with four-dimensional homothety groups.

Findings

No self-similar Bianchi VIII and IX tilted perfect fluid models exist.

The most general Bianchi VIII and IX spacetime with a four-dimensional homothety group is characterized.

Symmetry vector is not normal to surfaces of spatial homogeneity in these models.

Abstract

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.