Schrodinger theory of black holes

TL;DR

This paper derives a Schrödinger equation for Schwarzschild black holes, modeling them as quantum gravitational systems similar to hydrogen atoms, revealing discrete spectra for gravitational constants and suggesting space-time quantization.

Contribution

It introduces a novel two-particle quantum model of black holes, replacing singularities with a non-singular system and deriving quantum gravitational quantities with discrete spectra.

Findings

Black holes modeled as quantum gravitational systems analogous to hydrogen atoms.

Discrete spectra for gravitational constants, including a gravitational fine structure constant.

Black hole quantum states follow Schrödinger's theory, implying space-time quantization.

Abstract

The Schrodinger equation of the Schwarzschild black hole (SBH) is derived via Feynman's path integral approach by re-obtaining the same results found by the Author and collaborators in two recent research papers. In this two-particle system approach to BH quantum physics the traditional classical singularity in the core of the SBH is replaced by 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 other words, the SBH is the gravitational analog of the hydrogen atom and this could, in principle, drive to a space-time quantization based on a quantum mechanical particle approach. By following with caution the analogy between this SBH Schrodinger equation and the traditional Schrodinger equation of the s states (l=0) of the hydrogen atom, the SBH Schrodinger equation can be solved and discussed. The approach also permits us to find the quantum gravitational quantities which are the gravitational analogous of the fine structure constant and of the Rydberg constant. Remarkably, such quantities are not constants. Instead, they are dynamical quantities having well defined discrete spectra. In particular, the spectrum of the "gravitational fine structure constant" is exactly the set of non-zero natural numbers \mathbb{N}-\left\{ 0\right\} . Therefore, one argues the interesting consequence that the SBH results in a well defined quantum gravitational system, which obeys Schrodinger's theory: the "gravitational hydrogen atom".