The gravitational properties of a torus are investigated. It is shown that a torus can be formed from test particles orbiting in the gravitational field of a central mass. In this case, a toroidal distribution is achieved because of the significant spread of inclinations and eccentricities of the orbits. To investigate the self-gravity of the torus we consider the N-body problem for a torus located in the gravitational field of a central mass. It is shown that in the equilibrium state the cross-section of the torus is oval with a Gaussian density distribution. The dependence of the obscuring efficiency on torus inclination is found.
Abstract-Temporal and energy characteristics of the very-high-energy gamma-ray bursts from evaporating primordial black holes have been calculated by assuming that the photospheric and chromospheric effects are negligible. The technique of searching for such bursts on shower arrays is described. We show that the burst time profile and the array dead time should be taken into account to interpret experimental data. Based on data from the Andyrchy array of the Baksan Neutrino Observatory (Institute for Nuclear Research, Russian Academy of Sciences), we have obtained an upper limit on the number density of evaporating primordial black holes in a local region of space with a scale size of ∼ 10
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