Asymptotic behavior of the gravitational field and the nature of singularities in gowdy spacetimes

Abstract

In this work, we present results which support the Strong Cosmic Censorship Conjecture and some of the ideas of Belinskii, Khalatnikov, and Lifschitz. The results concern the behavior of the gravitational field in the neighborhood of singularities in the polarized Gowdy spacetimes. We rigorously show (using certain “energy” estimates) that as one approaches the singularity, the metric field of any of these vacuum solutions of Einstein's equations asymptotically approaches a solution of a truncated system of equations in which spatial curvature terms have been dropped. Hence, the gravitational fields, in a sense, spatially decouple near the singularity. Based on this asymptotic behavior, we also show that only in a very small subclass of the polarized Gowdy spacetimes is the curvature bounded near the singularity. Hence, the generic polarized Gowdy spacetime cannot be extended across a Cauchy horizon.