Quasi-normal modes: The ``electrons'' of black holes as ``gravitational atoms''? Implications for the black hole information puzzle
Summary: Some recent important results on black hole (BH) quantum physics concerning the \textit{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 one to naturally interpret QNMs as quantum levels in a semiclassical model. This is a model of BH somewhat similar to the historical semiclassical 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 a \textit{time dependent Schrödinger equation} which permits the final BH state to be a \textit{pure quantum} state instead of a mixed one. Thus, information comes out in BH evaporation in agreement with the assumption by 't Hooft that Schrödinger 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.
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