Generation of mass and scalar charge of supermassive black holes via the mechanism of scalar-gravitational instability

A mathematical model for the development of spherical perturbations in a cosmological medium of a scalar-charged fluid with a Higgs scalar field is investigated. The system of equations for the perturbations is decomposed into two independent subsystems. One of these, a system of ordinary differential equations, corresponds to the singular part of the perturbations and describes the evolution of the total mass and charge of a singular source, while the second—a system of partial differential equations with respect to the nonsingular parts of the perturbations—is analyzed. Exact solutions of the evolution equations for the total mass and charge near singular points of the background cosmological model are found. These solutions demonstrate the impossibility of a sufficiently rapid growth of the singular source mass at these points. Conversely, numerical integration of the evolution equations at nonsingular points of the cosmological model demonstrates the possibility of anomalously rapid growth of the singular mass (by a factor of 10²⁴ ) over times on the order of several hundred Planck times. The maximum rate of this process is achieved in models with small scalar particle charges g~ 10⁻⁵ and small values of the effective cosmological constant.