Article
Version 2
This version is not peer-reviewed
Black Hole as Gravitational Hydrogen Atom by Rosen’s Quantization Approach
Christian Corda
Version 1
: Received: 12 October 2018 / Approved: 18 October 2018 / Online: 18 October 2018 (10:39:33 CEST)
Version 2 : Received: 22 November 2018 / Approved: 23 November 2018 / Online: 23 November 2018 (14:29:57 CET)
Version 2 : Received: 22 November 2018 / Approved: 23 November 2018 / Online: 23 November 2018 (14:29:57 CET)
How to cite: Corda, C.; Feleppa, F. Black Hole as Gravitational Hydrogen Atom by Rosen’s Quantization Approach. Preprints 2018, 2018100413 (doi: 10.20944/preprints201810.0413.v2). Corda, C.; Feleppa, F. Black Hole as Gravitational Hydrogen Atom by Rosen’s Quantization Approach. Preprints 2018, 2018100413 (doi: 10.20944/preprints201810.0413.v2).
Abstract
We apply Rosen’s approach to the quantization of the gravitational collapse in the simple case of a pressureless “star of dust” and we find the gravitational potential, the Schroedinger equation and the solution for the collapse’s energy levels without any approximation. By applying the constrains for a black hole (BH), we found the analogous quantum quantities and the BH mass spectrum, again without any approximation. Remarkably, such a mass spectrum is the same which was found by Beken- stein in 1974. Finally, our approach permits to find the exact quantum representation of the Schwarzschild BH ground state at the Planck scale.
Subject Areas
Gravitational atom; quantum black hole; quantum levels; Schrodinger equation; mass spectrum.
Copyright: 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.
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