闭合半经典反弹的熵障碍
Entropy Obstruction to Closed Semiclassical Bounces
- Indian Institute of Technology Gandhinagar（印度理工学院甘地纳加尔分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明了一个有限Għ奇点定理：在紧致柯西切片半经典时空中，若区域条件超熵且存在离散最大光片，且另一区域稳健量子俘获，则未来柯西发展含不完备零测地线，从而排除闭合宇宙中的受控半经典反弹。
AI中文摘要：
我们证明了具有紧致柯西切片的半经典时空的一个有限$G\hslash$奇点定理。设一个紧致柯西切片被一个紧致曲面分为区域$B$和$C$。假设$B$是条件性超熵的，即$H_{\max,\mathrm{gen}}^\varepsilon(BC|C)>0$，从分割曲面朝向$B$的未来内向零边界是一个离散最大光片，且$C$是稳健量子俘获的。假设离散最大聚焦以及闭合光片的规则半经典端点，则$B$的未来柯西发展包含一个不完备的零测地线生成元。这与熵奇点定理相平行，其中超熵与内向光片的存在相结合，而稳健量子俘获在此提供了所需的额外有限$G\hslash$局部障碍。在闭合弗里德曼宇宙中，该定理排除了当收缩半球位于这样的光片上且包含比其边界所能支持的更多独立信息时，一个受控的半经典反弹。
英文摘要：
We prove a finite-$G\hslash$ singularity theorem for semiclassical spacetimes with compact Cauchy slices. Let a compact Cauchy slice be divided by a compact surface into regions $B$ and $C$. Suppose that $B$ is conditionally hyperentropic, $H_{\max,\mathrm{gen}}^\varepsilon(BC|C)>0$, that the future-inward null boundary from the dividing surface toward $B$ is a discrete max lightsheet, and that $C$ is robustly quantum trapped. Assuming discrete max-focusing and a regular semiclassical endpoint for a closing lightsheet, the future Cauchy development of $B$ contains an incomplete null generator. This parallels entropy singularity theorems in which hyperentropy is combined with the existence of an inward lightsheet, while robust quantum trapping supplies the additional finite-$G\hslash$ local obstruction needed here. In a closed Friedmann universe, the theorem excludes a controlled semiclassical bounce when a contracting hemisphere lies on such a lightsheet and contains more independent information than its boundary can support.
