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 3
: Received: 5 December 2019 / Approved: 6 December 2019 / Online: 6 December 2019 (04:14:35 CET)
Corda, C.; Feleppa, F. The Quantum Black Hole as a Gravitational Hydrogen Atom. Advances in Theoretical and Mathematical Physics 2022, 26, 3437–3562, doi:10.4310/atmp.2022.v26.n10.a4.
Corda, C.; Feleppa, F. The Quantum Black Hole as a Gravitational Hydrogen Atom. Advances in Theoretical and Mathematical Physics 2022, 26, 3437–3562, doi:10.4310/atmp.2022.v26.n10.a4.
Corda, C.; Feleppa, F. The Quantum Black Hole as a Gravitational Hydrogen Atom. Advances in Theoretical and Mathematical Physics 2022, 26, 3437–3562, doi:10.4310/atmp.2022.v26.n10.a4.
Corda, C.; Feleppa, F. The Quantum Black Hole as a Gravitational Hydrogen Atom. Advances in Theoretical and Mathematical Physics 2022, 26, 3437–3562, doi:10.4310/atmp.2022.v26.n10.a4.
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.
Keywords
Gravitational atom; quantum black hole; quantum levels; Schrodinger equation; mass spectrum.
Subject
Physical Sciences, Mathematical Physics
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.