Quantization of Gravitationally Bound Systems

Michael Fil’Chenkov,Yuri Laptev

doi:10.3390/universe7020030

Michael Fil’Chenkov, Yuri Laptev

Open Access

https://doi.org/10.3390/universe7020030

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Journal: Universe	Publication Date: Jan 30, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Peoples' Friendship University of Russia

Abstract

Some of the approaches to quantization in gravity theory concerning gravitationally bound systems are considered. Grades of quantization applicable to these systems have been classified in terms of quantum mechanics, quantum field theory, and quantum geometrodynamics. Energy levels for the graviatom, Lemaître’s atom, quantum gravitational collapse have been calculated, and relationships for the masses of bound system components, as well as Universe’s birth probabilities, are presented to exemplify the properties of gravitationally bound systems. Objects and processes in them have been analyzed to construct quantum models of compact astrophysical objects and the early Universe.

Highlights

There exist two approaches [1,2,3] towards quantizing gravity itself: a perturbative field-theoretical approach, wherein gravitons are introduced, and a non-perturbative geometrical approach.The perturbative quantum gravity proves to be non-renormalizable in the general case
Others have not found a wide application. They concern quantum mechanics in a gravitational field [5], quantum gravitational collapse [6], and quantum cosmology [7], when we deal with gravitationally bound systems, which are a subject of our investigation
The objects and processes in gravitationally bound systems correspond to these grades of quantization, as follows: graviatoms, which comprise miniholes that are capable of capturing elementary particles [13,14], the Universe’s birth from de Sitter’s vacuum, quantum gravitational collapse, and particle creation near horizons and in the early Universe

Summary

Introduction

There exist two approaches [1,2,3] towards quantizing gravity itself: a perturbative field-theoretical approach, wherein gravitons are introduced, and a non-perturbative geometrical approach. Others have not found a wide application They concern quantum mechanics in a gravitational field [5], quantum gravitational collapse [6], and quantum cosmology [7], when we deal with gravitationally bound systems, which are a subject of our investigation. This paper reports our results (Sections 3–6) concerning quantization in gravity theory, which are significant for bound quantum systems. They promise a major advance in understanding the general pattern of a consistent theory of gravity quantization

Quantization in Gravity Theory

Schrödinger’s Type Equations

System Component Masses

Conclusions