Behavior of homogeneous five-dimensional space-times

Abstract

The set of all spatially homogeneous (4+1)-dimensional cosmologies will be explored. We will utilize a classification of these space-times based on the actions of isometry groups on these manifolds. Several exact solutions of the Einstein equations will be derived. The possibilities of dimensional reduction and isotropization will be examined. Five-dimensional generalizations of the mixmaster universe will be developed. Finally, the Einstein equations in 4+1 dimensions will be viewed as a Hamiltonian system. The absence of chaotic solutions to these equations will be shown.