Abstrakt
Processes around astrophysical black holes are usually modeled with test (nongravitating) matter and fields. However, the very fact that the holes are "visible" implies that some matter has to be present there.
Even if very thin, it can influence the metric, mainly in higher derivatives, which should in turn affect its own behaviour, as well as motion of further (test) satellites. In particular, the geodesic dynamics, integrable in the fields of isolated stationary black holes, should become chaotic.
Here we consider exact static, axially and reflection- symmetric space-times of a Schwarzschild black hole surrounded by a thin disc or ring, and examine how the presence of the additional source affects the dynamics of free test particles using recurence analysis.