量子黑洞作为一个理论实验室，一个教学治疗的新方法
The quantum black hole as a theoretical lab, a pedagogical treatment of a new approach
摘要：
要正确地得到量子化黑洞的数学规则，远非易事。许多早期的论文都没有完全正确地得到它。广义相对论变换将远处的观察者（他只能探测到黑洞外的粒子）与本地观察者（他落入黑洞）的观察结果联系起来，必须以一对一的方式映射出量子态。如果一个人遵循教科书的规则，这是不正确的。这里主张要求非常严格的逻辑导致新的见解，如黑洞附近的时空拓扑的非平凡性。这样，人们可以试图弥补普朗克尺度下引力的直接实验证据的缺乏。值得注意的是，这种方法不需要像弦论或AdS/CFT理论那样的假设。我们只需要假设，只要史瓦西度规是正则的，量子场论就成立，并结合这样的要求，即只有那些将纯量子态一一映射到纯量子态的一般坐标变换才适用。
英文摘要：
Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects particles outside the hole) with the observations of a local observer (who falls into a black hole) must map the quantum states in a one-to-one way. This does not come out right if one follows text book rules. Here it is advocated that demanding very strict logic leads to new insights, such as the non-triviality of space-time topology near a black hole. This way one may attempt to make up for the lack of direct experimental evidence concerning gravitation at the Planck scale. It is noted that this approach does not require assumptions such as string theories or AdS/CFT conjectures. All we need to assume is the validity of quantum field theory wherever the Schwarzschild metric is regular, combined with the requirement that only those general coordinate transformations apply that map pure quantum states one-to-one onto pure quantum states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
