GEODESIC CHAOS AROUND BLACK HOLES WITH DISCS

In the fields of isolated stationary black holes, the geodesic dynamics is regular. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here we study the chaos induced by the presence of an additional source in the Schwarzschild space-time. Following the astrophysical motivation, we consider thin discs or rings lying symmetrically around the hole and describe the total fields in terms of exact static and axially symmetric solutions of Einstein’s equations. The character of geodesic dynamics can be revealed by Poincaré sections, Fourier spectra of the “vertical”-position time series and evolution of the test-particle “latitudinal action”.