Black Hole as Gravitational Hydrogen Atom by Rosen’s Quantization Approach

Christian Corda; Fabiano Feleppa

doi:10.20944/preprints201810.0413.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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)

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.

Gravitational atom; quantum black hole; quantum levels; Schrodinger equation; mass spectrum.

PHYSICAL SCIENCES, Astronomy & Astrophysics

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Black Hole as Gravitational Hydrogen Atom by Rosen’s Quantization Approach

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