Higher symmetries in a class of cosmological models

Abstract

A particular class of solutions of Einstein's field equations, in which the source is a perfect fluid and the geometry admits a two-parameter Abelian isometry group with spacelike orbits, is examined for the possible admission of higher symmetries. It is shown that in certain cases the geometry is spatially homogeneous, being either of the ‘orthogonal’ Bianchi type I or of the ‘tilted’ Bianchi-Behr type VIUh withh = −4, and that no other cases of higher symmetry (in the sense of isometry groups) are possible. The global behaviour of the Bianchi-Behr type VIUh, models is studied, and conformal diagrams are given. This investigation is extended to the case when additional homothetic vectors are admitted, and a parallel study of the global behaviour, complete with conformal diagrams, is provided. A brief argument also shows that, within the class considered, whenever the fluid flow-lines possess identical thermal histories, the geometry is necessarily spatially homogeneous.