Onset of geodesic chaos in the black-hole-disc system

Oldrich Semerak, Petra Sukova

Black holes assumed in galactic nuclei certainly dominate their surroundings gravitationally. However, even in non-active nuclei like that in our Galaxy, there is enough mass (in stars, gas and dust) to influence {\em its own} (and each others') motion in a non-negligible way. One of tiny but robust effects is that the geodesic motion, which is integrable in the field of an {\em isolated} Schwarzschild or Kerr black hole, becomes chaotic when some additional matter is present. Here we consider exact static and axially symmetric space-times generated by a Schwarzschild black hole surrounded by a thin, reflectionally symmetric disc or ring, in order to show how geodesic dynamics in such fields gradually grows chaotic when parameters of the system and of the massive test particles are changed. The global features of spreading of chaos in the phase space can be observed on Poincar\'e sections in dependence on several parameters. We are especially interested in the attributes of a single trajectory which reveals the type of the motion and can be obtained from the measured time series. The influence of additional noise is considered.