## Research
**Black holes in four and higher dimensions**
An important part of our research is concerned with the mathematical theory of black holes. We are particularly interested in constructing new exact solutions of Einstein's equations, describing black holes, and investigating their properties. In the past few years we have also focused on developing general mathematical results, which will elucidate our notion of black holes. Recently, a central contribution to the higher dimensional gravity - the black hole uniqueness theorems in higher dimensions, was achieved with the participation of a member of the group.
**Compact objects and alternative theories of gravity **
The physical properties, such as structure, stability, characteristic modes of oscillation, phase transitions etc., of different compact objects are studied numerically. The results can be applied for the verification of the studied alternative theories of gravity in the strong-field regime. In particular, our research in that field has been focused on black holes and soliton-like self-gravitating objects in the scalar-tensor theories of gravity with non-trivial scalar field.
** Gravitational lensing **
Gravitational lensing is a powerful method for the measurement of the physical characteristics of different compact self-gravitating objects. This effect can be used for the measurement of their mass, angular momentum, electric and magnetic charges and so on. On the bases of the data obtained through gravitational lensing observations different alternative theories of gravity could also be tested. Our research on that field is focused on the gravitational lensing of black holes and naked singularities both in the strong deflection and weak deflection regimes.
Another result of our group in that field is a relation between the gravitational lens parameters and the frequencies of quasi-normal modes of static, spherically symmetric black holes, which might have considerable observational applications among which the localization of sources of gravitational waves. |