Publikace ÚTF

Geodesic dynamics is regular in the fields of isolated stationary black holes. However, due to
the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations.
Here, we examine what amount of stochasticity is induced in Schwarzschild space–time by the
presence of an additional source. Following astrophysical motivation, we specifically consider
thin rings or discs lying symmetrically around the hole, and describe the total field in terms
of exact static and axially symmetric solutions of Einstein’s equations. The growth of chaos
in time-like geodesic motion is illustrated on Poincar´e sections, on time series of position or
velocity and their Fourier spectra, and on time evolution of the orbital ‘latitudinal action’. The
results are discussed in terms of dependence on the mass and position of the ring/disc and
on geodesic parameters (energy and angular momentum). In the Introduction, we also add an
overview of the literature.