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Based on the formulated and proven similarity properties of cosmologicalmodels based on a statistical system of degenerate scalarly charged fermions,as well as the previously identified mechanism of scalar-gravitationalinstability of cosmological models, a numerical-analytical study of theformation of supermassive black hole nuclei in the early Universe was carriedout. A mathematical model of the evolution of spherical perturbations isconstructed, on the basis of which the main regularities of the process ofevolution of collapsing masses and the dependence of the parameters of formingblack holes on the fundamental parameters of the cosmological model and thewavelength of gravitational perturbations are revealed. In this case, the massloss of the black hole due to quantum evaporation is taken into account. Astable tendency for the early formation of supermassive black hole nuclei inthe class of cosmological models under study is shown, and a close connectionbetween the growth of masses of spherical perturbations and the nature of thesingular points of these models is shown. Keywords: scalarly charged plasma,cosmological model, Higgs scalar field, gravitational stability, sphericalperturbations, black hole formation, evaporation.

Formation of supermassive nuclei of Black holes in the early Universe by the mechanism of scalar-gravitational instability. I. Local picture