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As far as I am aware, no stable orbits can exist inside of the event horizon. There is a region just outside of the event horizon (called the photon sphere) where the closest stable orbit can exist. This is about 50% larger than the diameter of the event horizon itself. It is at this point where objects travelling at the speed of light (i.e. photons) can enter a stable orbit. Any closer than that, and you'd have to exceed the speed of light to keep your orbit. Since that isn't possible, you fall in.
Is this a case of a stationary photon?
I personally don't think you can even get through the event horizon; I think that Hawking-type radiation gets more intense as you get close, and at the limit that tears you apart. The idea that you can cross the event horizon safely is based on the no-hair conjecture which completely ignores quantum mechanics.The point with a black hole there is actually a reference frame that matters; you're moving relative to the black hole, and towards the event horizon, there's nothing stopping QM forming an impenetrable barrier there.http://en.wikipedia.org/wiki/No-hair_theoremhttp://en.wikipedia.org/wiki/Black_hole_information_paradox