Is there any theoretical or empirical research about planetary systems with a black hole in their center?
Since planets are known to exist around neutron stars (e.g. see Wolcznan &amp; Frail (1992); and see the list of "pulsar planets" - technically, these were the first exoplanets ever discovered), then it is difficult to see any fundamental reason why there should not be examples orbiting black holes. 

In fact, since it is probably feasible to form black holes via direct collapse, without an associated supernova then maybe the hazards for planets are not so severe.

Against this, must be set the fact that black hole progenitors are likely to be more massive than neutron star progenitors and the role of winds and radiation on the formation of planets is still not well established.

Planets orbiting neutron stars are/were found from a timing analysis of pulsar signals. The same phenomenenon is not present for black holes and direct imaging or observing a transit is not remotely feasible at present.