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Registration Number

0219U004181, 0116U003662 , R & D reports

Title

The study of cosmological and astrophysical models of General Relativity and Kaluza-Klein theory, taking into account the pressure and the presence of the cosmological vacuum

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Head

Gladush Valentin Danilovich,

Registration Date

09-04-2019

Organization

Oles Honchar Dnipro National University

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The object of study is the motion of charged test particles in the field of a black hole and open singularity, spherically-symmetric configurations of the gravitational and electromagnetic fields, taking into account the cosmological vacuum and their quantization. The purpose of the work is to study the peculiarities of motion of charged test particles, the stability conditions of their equilibrium static states, the calculation of the frequency of particle oscillations around the equilibrium position; analyze the relationship between the space-time and mini-superspace description of spherically symmetric configurations of the gravitational and electromagnetic fields, study the geometry of the configuration space their sistems (including the cosmological constant), Dirac and Gitman-Tyutin quantization methods and the relationship between them. Research methods - differential-geometric methods of general relativity, methods for studying degenerate dynamical systems, quantization methods. The stability conditions for the equilibrium static states of particles above the central object are obtained; the calculated frequencies of their oscillations around the equilibrium position in the field of an anomalously charged object. A method has been developed for studying configuration spaces of the corresponding spherically symmetric systems of the electromagnetic and gravitational fields, methods of classical and quantum descriptions of the geometrodynamics of these systems. It is shown that the configuration space is flat and the solutions of the Einstein-Hamilton-Jacobi equations are obtained and investigated. The mass and charge operators are introduced and the solution of the eigenvalue problem of these operators is constructed, consistent with the solution of the Devitt equation. The developed methods and the results obtained can serve as the basis for further fundamental research in these areas. The results of research can also be used in the special course "Physical fields in the general relativity."

Product Description

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Головко Максим Геннадійович

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2020-04-02