Mathematical formulations of gravitational physics

Lie symmetry analysis and its application to astrophysics

The theory of structure formation in the early Universe

Gravitational lensing in cosmology

Chaos and critical phenomena in General Relativity

Computer algebra systems with application to general relativity

Gravitational waves in General Relativity

The first detection of gravitational waves in 2015 opened a new window on the Universe. Gravitational waves which approach Earth-based
detectors are extremely weak and, as such, very well described by the linearized Einstein's gravity theory. If full Einstein's equations
are taken into account new phenomena come into play. This 'territory' is mainly unexplored and is a subject of mathematical studies
conducted in our department:

In the standard cosmological model it is assumed that the matter is distributed homogeneously
in space. Although this model is consistent with a variety of astronomical observations, it brings us to some mysteries. To achieve the
agreement between the model predictions and the observations one should introduce the cosmological constant - the term in the Einstein
equations connected with the hypothetical form of matter called dark energy, which physical nature is unknown. In our department we study
the more general class of cosmological models, which admit the existence of matter inhomogeneities representing the large-scale
structures in the Universe. We study how these inhomogeneities could influence the cosmological observations. Some of our recent results
on this topic are: