Seminar

This report is devoted to mathematical modeling of spherically symmetric gravitating configurations of a scalar field with minimal coupling. We find analytical generalization of the methods of restored scalar potential and propose a general classification of scalar configurations. A comparative analytical and numerical analysis of vacuum black holes and static gravitating configurations of a classical scalar field (black holes, naked singularities, wormholes, and topological geons) is implemented. Scalar gravitating configurations are of interest as models of the spacetime geometry in the close vicinity of massive, strongly gravitating objects at the centers of galaxies, while the scalar field is considered as an effective model of dark matter. The main observed effects are related, firstly, to the motion of test particles (solar-mass stars) around the attracting centers, therefore, a significant part of this study is devoted to the numerical analysis of the parameters of their orbits. Secondly, models of tidal disruption of stars are constructed and it is shown that the mechanism of so-called tidal disruption events is completely different for black holes and naked singularities. In our numerical calculations, in particular, the method of covariant series in normal coordinates is used. In calculating the coefficients of covariant expansions of tensor fields in the normal neighborhood of a submanifold, an original algorithm was developed and its computational complexity was estimated. The algorithm is realised in the form of a program complex.

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