Quantum oscillations in the black hole horizon

A quantum model for the Schwarzschild black hole was recently proposed by applying Rosen's quantization approach to the historical Oppenheimer and Snyder gravitational collapse and by setting the constraints on the formation of the Schwarzschild black hole. An interesting picture emerges: the traditional Schwarzschild singularity is replaced by a quantum oscillator describing a nonsingular “two-particle” system where the two components, the “nucleus” and the “electron”, strongly interact with each other through a quantum gravitational interaction. In agreement with the de Broglie hypothesis, the “electron” is interpreted in terms of quantum oscillations of the black-hole horizon. In other words, the Schwarzschild black hole should be considered as a gravitational analogue of the hydrogen atom. In this paper, after a short review of our previous results, we analyze some of the consequences of this approach. We also show that, by performing a correct rescaling of the energy levels, the semiclassical Bohr-like approach to quantum black holes, previously developed by one of the authors (CC), is consistent with the results obtained here for large values of the black-hole principal quantum number. After this, Hawking radiation is analyzed by discussing its connection with the black-hole quantum structure. Finally, we conclude the paper by discussing the black-hole information problem and its possible resolution.