A Classification Theorem for Compact Cauchy Horizons in Vacuum Spacetimes

Explore a comprehensive classification theorem for the topology of compact, non-degenerate Cauchy horizons in time-orientable, smooth, vacuum 3+1-spacetimes in this 40-minute conference talk. Begin with a review of previous relevant results before delving into the main theorem. Learn about the four possible configurations for horizon generators: (i) all closed, (ii) two closed with others densely filling a two-torus, (iii) all densely filling a two-torus, or (iv) all densely filling the horizon. Discover how these configurations correspond to specific horizon manifold types: (i') Seifert manifold, (ii') lens space, (iii') two-torus bundle over a circle, or (iv') three-torus. Gain insight into the resolution of a problem posed by Isenberg and Moncrief for ergodic horizons, with the conclusion that in the three-torus case, the spacetime is the flat Kasner space.