Formation of Supermassive Nuclei of Black Holes in the Early Universe by the Mechanism of Scalar-Gravitational Instability. I. Local Picture\({}^{1}\)

On the basis of the formulated and proven similarity properties of cosmological models based on a statistical system of degenerate scalarly charged fermions, as well as the previously identified mechanism of scalar-gravitational instability of cosmological models, a numerical and analytical study of the formation of supermassive black hole nuclei in the early Universe is carried out. A mathematical model of the evolution of spherical perturbations is constructed, making itt possible to reveal the main regularities of the process of evolution of collapsing masses and the dependence of the parameters of forming black holes on the fundamental parameters of the cosmological model and the wavelength of gravitational perturbations. In this case, the mass loss of the black hole due to quantum evaporation is taken into account. A stable tendency for the early formation of supermassive black hole nuclei in the class of cosmological models under study is shown, and a close connection between the growth of masses of spherical perturbations and the nature of the singular points of these models is shown.