Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

Abstract

The Schrödinger equation of the Schwarzschild black hole (BH) shows that a BH is composed of a particle, the "electron", interacting with a central field, the "nucleus". Via de Broglie's hypothesis, one interprets the "electron" in terms of BH horizon's modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. Therefore, BHs are well defined quantum gravitational systems obeying Schrödinger's theory: the "gravitational hydrogen atoms". By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH descripted as a "gravitational hydrogen atom" is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having as radius the oscillating gravitational radius. Nontrivial consequences emerge from this result: i) BHs have neither horizons nor singularities; ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein-Gordon equation and the corresponding eigenvalues.

arXiv comment30 pages, accepted for publication in Communications in Theoretical Physics

References in corpus (39)

• Hawking Radiation as Tunneling
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Black Holes: Complementarity or Firewalls?
• The Stretched Horizon and Black Hole Complementarity
• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• AdS/CFT duality and the black hole information paradox
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Spectroscopy of the quantum black hole
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• The physical interpretation of the spectrum of black hole quasinormal modes
• Statistical interpretation of Bekenstein entropy for systems with a stretched horizon
• Black holes in an ultraviolet complete quantum gravity
• Information Preservation and Weather Forecasting for Black Holes
• Quantum Mechanics of Charged Black Holes
• Singularity avoidance by collapsing shells in quantum gravity
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• Black Holes as Quantum Membranes
• Embedding variables in the canonical theory of gravitating shells
• Quantum gravitational collapse: non-singularity and non-locality
• Time-Dependent Schrodinger Equation for Black Hole Evaporation: no Information Loss
• Non-local (but also non-singular) physics at the last stages of gravitational collapse
• Schrodinger formalism, black hole horizons and singularity behavior
• Precise model of Hawking radiation from the tunnelling mechanism
• Observations Supporting the Existence of an Intrinsic Magnetic Moment Inside the Central Compact Object Within the Quasar Q0957+561
• Effective state, Hawking radiation and quasi-normal modes for Kerr black holes
• Black holes as Gravitational Atoms
• Black Hole Complementarity and the Physical Origin of the Stretched Horizon
• Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzle
• Black hole area quantization
• From Planck area to graph theory: Topologically distinct black hole microstates
• On the quantization of the extremal Reissner-Nordstrom black hole
• Membrane paradigm realized?
• Quantum oscillations in the black hole horizon
• Physical origin of the dark spot at the image of supermassive black hole SgrA* revealed by the EHT collaboration
• Hydrogen-like Spectrum of Spontaneously Created Brane Universes with deSitter Ground State
• The quantum black hole as a gravitational hydrogen atom

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