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I assume such a system would be hard to detect due to a lack of radiation, at least if the vicinity of the black hole does not contain a lot of mass which falls into it over time, thus creating (a lot of) radiation.

Since black hole formation in a supernova explosion is a process which destroys any planetary system around its original star, any planetary system around a black hole must have formed after black hole formation.

A few objections come to mind off-the-cuff: Because black holes have a large mass there is a minimum distance for planetary orbits below which they would disintegrate due to tidal forces. This may interfere with the usual evolution of planets (they clear their orbits and kick out interfering bodies, for example), because their "orbital space volume" becomes too large for them to keep clean, and the orbital period becomes long.

Is anything known or is there any speculation about such systems?

Peter - Reinstate Monica
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    Possible duplicate of Orbiting around a black hole – J. Chomel Jul 07 '17 at 08:45
  • I don't think this is a duplicate. The proposed duplicate asks a general question, whether objects can orbit a black hole. This asks a much more specific question, whether black holes can have planets. – David Hammen Jul 07 '17 at 12:19
  • You're misunderstanding the meaning of "planet" . All the stars in a galaxy are planets orbiting the central black hole. – Carl Witthoft Jul 07 '17 at 12:35
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    @CarlWitthoft I think it is safe to say that celestial bodies large enough to maintain nuclear fusion are not planets. I also doubt that they have cleared their galactic orbits or forced other objects in their orbit into resonance. I'm not sure where you see a misunderstanding -- an orbit is not a sufficient condition for a body to be a planet. – Peter - Reinstate Monica Jul 07 '17 at 12:57
  • @J.Chomel Well, I was not doubting the general physical possibility (as the other OP). I was wondering whether there is theoretical or practical research about it. I'll reword the title. – Peter - Reinstate Monica Jul 07 '17 at 12:59
  • @PeterA.Schneider the current IAU standards (which neither I nor Phil Plait particularly agree with) only allow Solar objects to be considered. I see no reason not to use "planet" at the very least as an adjective to distinguish stars in a closed conic section path vs. non-captured stars. – Carl Witthoft Jul 07 '17 at 13:04
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    @CarlWitthoft - No matter what you definition you want to use for what qualifies as a "planet", stars are not planets. – David Hammen Jul 07 '17 at 13:10
  • @CarlWitthoft (Almost?) everything orbits something... – Peter - Reinstate Monica Jul 07 '17 at 18:56

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Since planets are known to exist around neutron stars (e.g. see Wolcznan & 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.

ProfRob
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  • Well, nuts. +1 nuts, but nuts. I was about to write up a very similar answer. It might be worthwhile to add that those exoplanets discovered by Wolcznan & Frail were the very first exoplanets to be discovered. – David Hammen Jul 07 '17 at 13:04
  • And we saw planets orbiting the black hole in "Interstellar" so they have to exist. (Just joking, but they did "science" that movie pretty well. You can even buy a book by Kip Thorne on "The Science of Interstellar".) – Jack R. Woods Jul 11 '17 at 04:41
  • It just occurred to me that there may also be primordial black holes of pretty arbitrary sizes (in particular, smaller ones than the remains of a massive star). AFAIK it's all pretty speculative; smaller black holes may be hard to observe so there is no good data for principle reasons.If one with the mass of a planet would reverse roles and planet-like orbit a regular star, enough occasional matter may fall in that it becomes visible at times, like its larger cousins, from the resulting radiation. – Peter - Reinstate Monica Dec 08 '20 at 12:22