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Some recent important results on black hole (BH) quantum physics concerningthe BH effective state and the natural correspondence between Hawking radiationand BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such acorrespondence permits to naturally interpret QNMs as quantum levels in asemi-classical model. This is a model of BH somewhat similar to the historicalsemi-classical model of the structure of a hydrogen atom introduced by Bohr in1913. In a certain sense, QNMs represent the "electron" which jumps from alevel to another one and the absolute values of the QNMs frequencies"triggered" by emissions (Hawking radiation) and absorption of particlesrepresent the energy "shells" of the "gravitational hydrogen atom". Importantconsequences on the BH information puzzle are discussed. In fact, it is shownthat the time evolution of this "Bohr-like BH model" obeys to a time dependentSchr\"odinger equation which permits the final BH state to be a pure quantumstate instead of a mixed one. Thus, information comes out in BH evaporation, inagreement with the assumption by 't Hooft that Schr\"oedinger equations can beused universally for all dynamics in the universe. We also show that, inaddition, our approach solves the entanglement problem connected with theinformation paradox. We emphasize that Bohr model is an approximated model ofthe hydrogen atom with respect to the valence shell atom model of full quantummechanics. In the same way, we expect the Bohr-like BH model to be anapproximated model with respect to the definitive, but at the present timeunknown, BH model arising from a full quantum gravity theory.

Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzle