准正规模：黑洞的“电子”是“引力原子”？黑洞信息之谜的含义
Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzle
摘要：
对近年来黑洞量子物理中有关黑洞有效态以及霍金辐射与黑洞准简正模之间的自然对应关系的一些重要结果进行了评述、澄清和改进。这样的对应允许自然地将QNM解释为半经典模型中的量子能级。这是一个BH模型，有点类似于玻尔在1913年提出的氢原子结构的半经典模型。在某种意义上，QNM代表从一个能级跳到另一个能级的“电子”，由粒子的发射（霍金辐射）和吸收“触发”的QNM频率的绝对值代表“引力氢原子“的能量“壳”。BH信息之谜的重要后果进行了讨论。事实上，它表明，这种“Bohr类BH模型”的时间演化服从一个时间依赖的薛定谔方程，它允许最终的BH状态是一个纯的量子态，而不是一个混合的。因此，信息来自BH蒸发，与特胡夫特的假设一致，即薛定谔方程可以普遍用于宇宙中的所有动力学。我们还表明，此外，我们的方法解决了纠缠问题与信息悖论。我们强调玻尔模型是氢原子相对于全量子力学价壳层原子模型的一种近似模型。同样地，我们期望类玻尔BH模型是一个近似模型，相对于确定的，但目前未知的，BH模型产生于一个完整的量子引力理论。
英文摘要：
Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such a correspondence permits to naturally interpret QNMs as quantum levels in a semi-classical model. This is a model of BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. In a certain sense, QNMs represent the "electron" which jumps from a level to another one and the absolute values of the QNMs frequencies "triggered" by emissions (Hawking radiation) and absorption of particles represent the energy "shells" of the "gravitational hydrogen atom". Important consequences on the BH information puzzle are discussed. In fact, it is shown that the time evolution of this "Bohr-like BH model" obeys to a time dependent Schrödinger equation which permits the final BH state to be a pure quantum state instead of a mixed one. Thus, information comes out in BH evaporation, in agreement with the assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe. We also show that, in addition, our approach solves the entanglement problem connected with the information paradox. We emphasize that Bohr model is an approximated model of the hydrogen atom with respect to the valence shell atom model of full quantum mechanics. In the same way, we expect the Bohr-like BH model to be an approximated model with respect to the definitive, but at the present time unknown, BH model arising from a full quantum gravity theory.
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