标题： 紧致的柯西视界具有恒定的表面引力 显示英文标题

标题： Compact Cauchy horizons admit constant surface gravity

摘要： 我们证明，在任何时空维度下，并在零能量条件下，每个完全测地的连通光滑紧致类光超曲面（因此每个紧致的柯西视界）都存在一个光滑的类光切向量场，其表面引力为常数。 也就是说，我们通过证明如果存在一条完整的生成曲线，则存在一个光滑的未来指向的测地类光切向量场，从而解决了开放的退化情况。 该结果可以表述为一个特定上同调方程的存在性结果。 证明使用了遍历理论、霍德格理论和黎曼流理论的元素。 我们强调，值得注意的是，这些结果实际上只需要零能量条件，而以前的工作在Killing情况或非退化情况下，已经假设了更强的主导能量条件。 显示英文摘要

摘要： We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular cohomological equation. The proof uses elements of ergodic theory, Hodge theory and Riemannian flow theory. We emphasize that, remarkably, these results really require only the null energy condition, whereas previous works assumed, already in the Killing or the non-degenerate case, the stronger dominant energy condition.