We prove that the surface gravity of a compact non-degenerate Cauchy horizon in a smooth vacuum spacetime, can be normalized to a non-zero constant. This result, combined with a recent result by Oliver Petersen and Istvan Racz, end up proving the Isenberg-Moncrief conjecture on the existence of Killing fields, in the smooth differentiability class. The well known corollary of this, in accordance with the strong cosmic censorship conjecture, is that the presence of compact Cauchy horizons is a non-generic phenomenon. Though we work in 3+1, the result is valid line by line in any n+1-dimensions.

中文翻译：

---

关于柯西紧凑视界光滑时空杀戮场的存在性

我们证明了在光滑真空时空中的致密非简并柯西视界的表面引力可以归一化为非零常数。这一结果与 Oliver Petersen 和 Istvan Racz 最近的结果相结合，最终证明了 Isenberg-Moncrief 猜想关于在平滑可微性类中存在 Killing 场。根据强大的宇宙审查猜想，其众所周知的推论是，致密柯西视界的存在是一种非一般现象。虽然我们在 3+1 中工作，但结果在任何 n+1 维度中都是有效的。