Strong Cosmic Censorship and the Stability of AVTD Behavior in Cosmological Space-Times

The Strong Cosmic Censorship Conjecture (SCCC) suggests that the “singularities” in cosmological space-times are generically characterized by unbounded curvature so that consequently these space-times generically cannot be extended beyond their maximal domains of dependence. One of the most effective tools for proving SCCC holds for a family of cosmological solutions of Einstein’s equations is to verify that these solutions all exhibit Asymptotically Velocity Term Dominated (AVTD) behavior in a neighborhood of their singularities. After presenting some background history of known results and conjectures concerning the behavior of the gravitational field near the singularity in cosmological space-times, we discuss recent work done with collaborators, as well as other recent results by others which show that AVTD behavior does occur in an open set of solutions within certain families in a neighborhood of the Kasner solutions.