The Isenberg–Moncrief conjecture for smooth vacuum spacetimes in 3+1 dimensions

Working draft. We prove that a compact Cauchy horizon in a smooth, time-oriented, four-dimensional vacuum spacetime cannot have a complete generator. Combined with the non-degenerate theorems of Bustamante–Reiris, Gurriaran–Minguzzi, Petersen–Rácz and Petersen, this yields the Isenberg–Moncrief conjecture in smooth 3+1 vacuum: every compact Cauchy horizon is a smooth Killing horizon with constant non-zero surface gravity.