Space-time and configuration manifolds of a spherically-symmetric system of gravitational and electromagnetic fields
Gladush V.D., Holovko M.H.
We investigate the space-time and configuration manifolds of a spherically symmetric system of gravitational and electromagnetic fields. For that, we construct the action and introduce dynamic quantities and relations for the field system under consideration. Then, additional physical quantities - the total mass and charge are introduced. We note, that the Poisson brackets of the total mass with the Hamiltonian function is zero in the weak sense. In order to make the transition into the configuration space, we exclude the non-dynamic degree of freedom from the action with the help of the Hamiltonian constraint. Herewith the Einstein-Hamilton-Jacobi equation is constructed and the structure of its solution compatible with the laws of conservation of total mass and charge is investigated. It turns out that the minisuperspace is flat, and therefore the solutions of the Einstein equations correspond to a bundle of straight lines in the minisuperspace. Their intersection with the light cone of minisuperspace corresponds to the horizons of events in the space-time of a charged black hole. The quantization of the fields system under consideration is analogous to the quantization of a free particle in a three-dimensional pseudo-Euclidean space. Using the Dewitt equations and the eigenvalue equations for the mass and charge operators, we construct a wave function of the field configuration. As a result, we obtain the model of a charged black hole with a continuous mass and charge spectra.
Keywords: spherical-symmetric configurations, minisuperspace, Hamilton operator, mass and charge operators, compatibility condition.
UDC: 530.12; 531.51
PACS: 04.40.Nr, 04.60.K
Please cite this article in English as: Gladush V.D., Holovko M.H. Space-time and configuration manifolds of a spherically-symmetric system of gravitational and electromagnetic fields. Space, Time and Fundamental Interactions, 2018, no. 2, pp. 28–48.