Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure

ANALYSIS OF PERSONAL FACTORS INFLUENCING THE LABOR COSTS OF EMPLOYEES OF THE SUPERVISORY ACTIVITIES OF THE MINISTRY OF EMERGENCY SITUATIONS OF RUSSIA

Background. The paper raises the problem of insufficient provision of supervision units of the Ministry of Emergency Situations of Russia with an inspection staff, as well as personal factors that affect labor costs. Materials and methods. Econometric methods (survey, variance and correlation analysis) were used to determine the level of influence of personal factors on labor costs during routine inspections. Results. The level of correlation between the time of the control (supervisory) event and such personal factors as: specialty, number of higher educations and service experience in the federal state fire supervision bodies is determined. Conclusions. The results of the study will make it possible to predict the labor costs for conducting inspections by various categories of employees, and can also be used as the basis for calculating the optimal number of control (supervisory) measures