Exterior differential system for cosmological G_2 perfect fluids and geodesic completeness

Abstract

In this paper a new formalism based on exterior differential systems is derived for perfect-fluid spacetimes endowed with an abelian orthogonally transitive G_2 group of motions acting on spacelike surfaces. This formulation allows simplifications of Einstein equations and it can be applied for different purposes. As an example a singularity-free metric is rederived in this framework. A sufficient condition for a diagonal metric to be geodesically complete is also provided.