标题： 从奥本海默和斯奈德引力坍缩的量子化得到的黑洞的薛定谔和克莱因-戈登理论 显示英文标题

标题： Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

摘要： 史瓦西黑洞（BH）的薛定谔方程表明，一个黑洞由一个“电子”粒子与中心场“原子核”相互作用组成。 通过德布罗意假设，“电子”可以用黑洞视界的模式来解释。 量子引力效应在史瓦西尺度上而不是普朗克尺度上修改了黑洞的半经典结构。 这个黑洞薛定谔方程与氢原子s态的薛定谔方程之间的类比使我们能够求解相同的方程。 因此，黑洞是遵循薛定谔理论的良好定义的量子引力系统：即“引力氢原子”。 通过将黑洞薛定谔方程中的势能识别为球对称壳的引力能，量子黑洞似乎呈现出不同的性质。 黑洞是由物质凝聚在视表面上而产生的自相互作用、高度激发、球对称、质量巨大的量子壳，具体实现了膜模型。 描述为“引力氢原子”的量子黑洞是真实量子黑洞的虚构数学表示，即具有振荡引力半径作为半径的量子质量壳。 由此得出的非平凡结果如下：i）黑洞既没有视界也没有奇点；ii）黑洞蒸发过程中不存在信息丢失，也不存在黑洞互补性或黑洞火墙悖论。 这些结果与霍金、瓦兹、米特拉等人的先前结果一致。 最后，黑洞薛定谔方程的狭义相对论修正给出了黑洞克莱因-戈登方程及其相应的本征值。 显示英文摘要

摘要： The Schr\"odinger equation of the Schwarzschild black hole (BH) shows that a BH is composed of a particle, the "electron", interacting with a central field, the "nucleus". Via de Broglie's hypothesis, one interprets the "electron" in terms of BH horizon's modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schr\"odinger equation and the Schr\"odinger equation of the s states of the hydrogen atom permits us to solve the same equation. Therefore, BHs are well defined quantum gravitational systems obeying Schr\"odinger's theory: the "gravitational hydrogen atoms". By identifying the potential energy in the BH Schr\"odinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH descripted as a "gravitational hydrogen atom" is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having as radius the oscillating gravitational radius. Nontrivial consequences emerge from this result: i) BHs have neither horizons nor singularities; ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schr\"odinger equation give the BH Klein-Gordon equation and the corresponding eigenvalues.