The speed of light is the upper limit at which conventional matter can travel. However, jet streams propel "material (...) at a significant fraction of the speed of light" (Wikipedia).
Let me rephrase the question, as I have made a mistake. Do we know what exactly emits the black hole in a jet stream?
And if they emit something than they put this matter back into this universe, which will then again serve as potential matter they could suck in.