* Stationary spacetimes

Elliptical PDE with a free boundary condition, rotating relativistic polytropy.

* 3 + 1 formulation of the Einstein equations

The most important variants, mathematical requirements for systems of hyperbolic PDE, initial data for numerical relativity, the boundary conditions.

* Critical phenomena in gravitational collapse

Spherically symmetric gravitational collapse, choice of coordinates, numerical methods for the study of the critical behavior.

* Black-hole numerical spacetimes

Representation of black holes in the initial data and during the simulation, interpretation of the results of numerical simulations, black hole horizons, emitted gravitational waves.

Basic numerical methods for solving Einstein equations of general relativity. For the 4th and 5th year of TF study.