TOWARD THE QUANTIZATION OF BLACK HOLES - Gladush, V. D. (Одеські астрономічні публікації, 2016)
In order to construct a quantum model of black hole (BH), we introduce a modified description of classical space-time BH (the Schwarzschild solution). We develop the Lagrangian formalism of the vacuum gravitational field in spherically symmetric space-time, divided on the two regions: R- and Tregions. Initial metrics in their regions are taken in the scale-invariant form and depend on a timelike coordinate in T-region and space-like coordinate in R-region. We introduce the Hamiltonian and mass function, which corresponding evolutional coordinate (t or r) in each of regions. Their Poisson brackets are proportional Hamiltonian constraint. Further we construct the quantum operators of Hamilton and masse. Their commutator are proportional to the Hamilton operator. System of Wheeler-De Witt equation and equation on the own values of mass operator, together with the compatibility condition, allow to find wave functions in every region. These wave functions form the common wave function of BH with the continuous masse spectrum