arXiv subjects

A. D. Kapustin

Publications and source records attributed to A. D. Kapustin.

4 recordsLinked to original sources

arXiv2023

Gravity as embedding theory and the distribution of matter in galaxies

The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to more general field equations than Einstein's equations. By writing them in the form of Einstein's equations with the contribution of additional fictitious matter, one can try to interpret this matter as dark matter. In order to study the behavior of this fictitious matter near the centers of real galaxies, we discuss an analytical method of obtaining corresponding matter density profiles. This method is based on the consideration of the distribution function of particles over all possible trajectories and allows us to estimate the type (core or cusp) of the emerging density profile.

gr-qc↗

arXiv2022

Analytical analysis of the origin of core-cusp matter density distributions in galaxies

We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the central slope of density profile and the near-origin behavior of the angular momentum distribution function. We consider both a spherically symmetric (on average) matter distribution as well as deviations from it. If the density profile forms in a background of spherical gravitation potential then a core-type distribution arises. A regular matter may behave in such way if the background potential was formed by the dark matter. In the presence of deviation from spherical symmetry the formation of cusp-type distribution is possible. Moreover, a reduction of spherical symmetry to the axial one leads to a less steep cusp profile. The complete symmetry breaking (which corresponds, in particular, to the common setup of numerical simulations), leads to a steeper cusp profile.

gr-qc↗

arXiv2020

Explicit isometric embeddings of black holes geometry with non-singular matter distribution

The work is devoted to the construction of explicit embeddings for the metrics of the black holes, formed by nonsingular matter distribution. One of the possible examples of such type of solutions is regular black hole. Using the existing classification of minimal symmetric embeddings of the Schwarzschild metric as a base, we construct embeddings for regular black holes with de Sitter interior. Another simple example is black hole, formed by collapsing homogeneous spherically symmetric cloud of dustlike matter. We discuss embeddings for two variants of such black holes - the one with the eternally existing horizon, when dust ball never leaves the interior of the horizon, and another variant with the dynamically forming horizon.

gr-qc↗

arXiv2020

Explicit isometric embeddings of collapsing dust ball

The work is devoted to the search for explicit isometric embeddings of a metric corresponding to the collapse of spherically symmetric matter with the formation of a black hole. Two approaches are considered: in the first, the embedding is constructed for the whole manifold at once; in the second, the idea of a junction of solutions, obtained separately for areas inside and outside the dust ball, is used. In the framework of the first approach, a global smooth embedding in 7D space with a signature (2 + 5) was constructed. It corresponds to the formation of the horizon as a result of matter falling from infinity. The second approach generally leads to an embedding in 7D space with the signature (1 + 6). This embedding corresponds to the case when matter flies out of a white hole with the disappearance of its horizon, after which the radius of the dust ball reaches its maximum, and then a collapse occurs with the formation of the horizon of a black hole. The embedding obtained is not smooth everywhere --- it contains a kink on the edge of the dust ball, and {also, it is} not quite global. In the particular case, when the maximum radius of the dust ball coincides with the radius of the horizon, it is possible to construct a global smooth embedding in a flat 6D space with a signature (1 + 5).

gr-qc↗