标题： 事件视界的正则性与面积定理 显示英文标题

标题： Regularity of Horizons and The Area Theorem

摘要： 我们证明了，在满足零能量条件的时空中，未来事件视界的截面面积在以下任何一种情况下都随着未来而单调不减：1）视界是未来的测地线完备的；2）视界是在全局双曲时空中的黑洞事件视界，并且存在一个“H-正则”的Scri正 conformal 完备；3）视界是在具有全局双曲 conformal 完备的时空中的黑洞事件视界。 （还建立了在较弱假设下的相关结果。） 这扩展了 Hawking 的一个定理，在该定理中似乎假设了事件视界的分段光滑性。 没有对宇宙常数或其符号做出任何假设。 当面积不等式中的等号成立时，我们证明了事件视界相关部分的光滑性或解析性——这在静态黑洞理论以及紧致柯西视界的结构方面都有应用。 在证明过程中，我们建立了一些关于视界可微性质的新结果。 显示英文摘要

摘要： We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under any one of the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a ``H-regular'' Scri plus; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. No assumptions about the cosmological constant or its sign are made. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained - this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.