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

Abstract

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 Schr\"odinger 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 Schr\"oedinger 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.