Publikace ÚTF

We continue the study of time-like geodesic dynamics in exact static, axially and reflection
symmetric space–times describing the fields of a Schwarzschild black hole surrounded by thin
discs or rings. In the first paper of this series, the rise (and decline) of geodesic chaos with
ring/disc mass and position and with test particle energy was revealed on Poincar´e sections and
on time series of position or velocity and their power spectra. In the second paper, we compared
these results with those obtained by two recurrence methods, focusing on ‘sticky’ orbits whose
different parts show different degrees of chaoticity. Here, we complement the analysis by
using several Lyapunov-type coefficients which quantify the rate of orbital divergence. After
comparing the results with those obtained by the previous methods, we specifically consider a
system involving a black hole surrounded by a small thin disc or a large ring, having in mind
the configuration which probably occurs in galactic nuclei. Within the range of parameters
which roughly corresponds to our Galactic centre, we found that the black hole accretion
disc does not have a significant gravitational effect on the dynamics of free motion at larger
radii, while the inner circumnuclear molecular ring (concentrated above 1 pc radius) can only
induce some irregularity in motion of stars (‘particles’) on smaller radii if its mass reaches 10
to 30 per cent of the central black hole (which is the upper estimate given in the literature), if
it is sufficiently compact (which does not hold but maybe for its inner rim) and if the stars can
get to its close vicinity. The outer dust ring between 60 and 100 pc appears to be less important
for the geodesic dynamics in its interior.