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...     

Tiled Orders and Frobenius Rings

Mathematical Notes -     

Associativity of crossed products by partial actions, enveloping actions and partial representations

Given a partial action of a group on an associative algebra , we consider the crossed product . Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of obtained in the context of -algebras. In particular, we prove that is associative, provided that is semiprime. We also give a criterion for the existence of a global extension of a given partial action on an algebra, and use crossed products to study relations between partial actions of groups on algebras and partial representations. As an application we endow partial group algebras with a crossed product structure.

     

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.     

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.     

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.     

Excitation of a rectangular waveguide by pulsed electric and magnetic currents

We consider the problem of excitation of electromagnetic fields by electric and magnetic currents that are present in a rectangular waveguide. The space-time Green’s functions are obtained for a waveguide with ideally conducting walls. The primary attention is given to analysis of the energy spectrum of radiation and the influence of the finite duration of the current pulse and the finite dimensions of the conductor with the current on the above spectrum. It is shown that the influence of the above properties on the spectrum is weak at low frequencies and increases with frequency. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 4, pp. 456–468, April, 1998.