Geodesic dynamics in the fields of black holes surrounded by discs

One of the basic tasks of general relativity is to calculate the motion of free test particles by integrating the geodesics equation. In the field of an iso- lated stationary black hole, the problem is fully integrable. However, the pres- ence of any other source of gravitation disrupts this property and the geodesic motion may become chaotic. In the following work we study the dynamics of motion around a Schwarzschild black hole surrounded by inverted Kuzmin- Toomre disks. To integrate the geodesics equation, we have developed a new code and investigated in detail some numerical methods, in particular, we com- pared Runge-Kutta methods and modified symplectic integrators.