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Advances in High Energy Physics
Volume 2015, Article ID 867601, 16 pages
http://dx.doi.org/10.1155/2015/867601
Review Article

Quasi-Normal Modes: The “Electrons” of Black Holes as “Gravitational Atoms”? Implications for the Black Hole Information Puzzle

1Physics Department, IURS “Santa Rita”, Via Trasaghis 18/E, 00188 Roma, Italy
2Austro-Ukrainian Institute for Science and Technology, Wiedner Hauptstrasse 8-10/136, 1040 Wien, Austria
3International Institute for Applicable Mathematics & Information Sciences (IIAMIS), B. M. Birla Science Centre, Adarsh Nagar, Hyderabad 500 463, India

Received 26 February 2015; Accepted 25 March 2015

Academic Editor: Maxim Khlopov

Copyright © 2015 Christian Corda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

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 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 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.