Velocity-Dominated Singularities in Irrotational Dust Cosmologies

Abstract

We consider irrotational dust solutions of the Einstein equations. We define ``velocity-dominated'' singularities of these solutions. We show that a velocity-dominated singularity can be considered as a three-dimensional manifold with an invariantly and uniquely defined inner metric tensor, extrinsic curvature tensor, and scalar bang time function. We compute this structure for a variety of known exact models. The structure of the singularity uniquely determines the solution in a certain class of spatially inhomogeneous models. We briefly discuss the b boundary (Schmidt boundary). In an appendix we generalize conformal transformations to ``stretch'' transformations and calculate the curvature form of a stretched metric.