On Strong Cosmic Censorship

For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities found in most solutions of Einstein's gravitational field equations: Are such singularities generically characterized by unbounded curvature? Is the existence of a Cauchy horizon (and the accompanying extensions into spacetime regions in which determinism fails) an unstable feature of solutions of Einstein's equations? In this short review article, after briefly commenting on the history of the SCC conjecture, we survey some of the progress made in research directed either toward supporting SCC or toward uncovering some of its weaknesses. We focus in particular on model versions of SCC which have been proven for restricted families of spacetimes (e.g., the Gowdy spacetimes), and the role played by the generic presence of Asymptotically Velocity Term Dominated behavior in these solutions. We also note recent work on spacetimes containing weak null singularities, and their relevance for the SCC conjecture.
Comment: Accepted for publication in Surveys in Differential Geometry, Volume 20