It strikes me that there are some similarities between a black hole and the disc used for the Arago spot experiments. Black holes (or their event horizons) are spherical, so should cast a circular shadow. Have there been any observations of bright spots in the centre of a black hole? If so, would these be useful for astronomy, like a supersized Aragoscope?
I have read that the shadowing object has to be very precisely circular, so I am not sure if a black hole is circular enough. Oblateness caused by rotation might distort the event horizon? There might also be issues with relativity around the fringes of the black hole. I don't have a clear concept of how gravitational lensing and Fresnel diffraction would work together.