Modeling the motion of a bright spot in jets from black holes M87* and SgrA*

General Relativity and Gravitation - In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these...     

Dark matter annihilation in the Galaxy

The awaited dark matter (DM) neutralino annihilation signal from the galactic halo crucially depends on the presence of small-scale clumps. A mass function of the DM small-scale clumps is calculated in the standard cosmological scenario. The final distribution of clumps in the Galaxy is influenced by their tidal destruction. The basic sources of clump destruction are (i) clumps of larger scales, (ii) the gravitational field of the galactic disk, (iii) the stars in the galactic bulge, and (iv) the stars in the galactic halo. The destruction of clumps due to their mutual tidal interactions is important at earl stages of hierarchical clustering and the galactic halo formation. The clumps surviving through the hierarchical clustering are continuously destroyed by interactions with the galactic disk and stars. It is shown that, among the Moon or Earth mass DM clumps surviving through the hierarchical clustering, only 20% will further survive near the Sun’s position mainly because of the tidal destruction by the galactic disk. This reduction of DM clump density significantly diminishes the expected DM annihilation signal from the galactic halo. The text was submitted by the authors in English.     

Tiled Orders and Frobenius Rings

Mathematical Notes -     

Molecular structure of (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine oxide. Synthesis of (3,5-diallylisocyanuratomethyl)phosphine sulfides

X-Ray study of the (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine oxide showed that the phosphorylmethyl group is bonded to the nitrogen atom of the cycle. Reaction of the tris(chloromethyl)phosphine sulfide with sodium diallylisocyanurate gave (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine sulfide, and treatment of the tris(3,5-diallylisocyanuratomethyl)phosphine oxide with phosphorus pentasulfide gave a tris(3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine sulfide.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1446–1448, August, 1993.     

Superdense dark matter clumps from superheavy particles

We describe some specific but reasonable conditions for the formation of superdense clumps (or minihalos) of dark matter. Such clumps can be produced by several mechanisms, most notably by spiky features in the spectrum of density perturbations. Being produced very early during the radiation-dominated epoch, these clumps evolve as isolated objects. They do not belong to hierarchical structures for a long time after production and are therefore not destroyed by tidal interactions during the formation of larger structures. If the clumps are constituted of superheavy dark matter particles, then the evolution of their central part can lead to a “gravithermal catastrophe,” increasing the central density and thus the annihilation signal. As a result, annihilations of superheavy neutralinos in dense clumps may lead to observable fluxes of annihilation products in the form of ultrahigh-energy particles.     

The accretion of dark energy onto a black hole

The stationary, spherically symmetric accretion of dark energy onto a Schwarzschild black hole is considered in terms of relativistic hydrodynamics. The approximation of an ideal fluid is used to model the dark energy. General expressions are derived for the accretion rate of an ideal fluid with an arbitrary equation of state p = p(ρ) onto a black hole. The black hole mass was found to decrease for the accretion of phantom energy. The accretion process is studied in detail for two dark energy models that admit an analytical solution: a model with a linear equation of state, p = α(ρ ? ρ₀), and a Chaplygin gas. For one of the special cases of a linear equation of state, an analytical expression is derived for the accretion rate of dark energy onto a moving and rotating black hole. The masses of all black holes are shown to approach zero in cosmological models with phantom energy in which the Big Rip scenario is realized.     

Possible types of the evolution of vacuum shells around the de Sitter space

All possible evolution scenarios of a thin vacuum shell surrounding the spherically symmetric de Sitter space have been determined and the corresponding global geometries have been constructed. Such configurations can appear at the final stage of the cosmological phase transition, when isolated regions (islands) of the old vacuum remain. The islands of the old vacuum are absorbed by the new vacuum, expand unlimitedly, or form black holes and wormholes depending on the sizes of the islands as well as on the density and velocity of the shells surrounding the islands.     

Rings with finite decomposition of identity

A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also present a brief survey of some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given.