What would things would look like if you could stand on a black hole at such a distance that the light bouncing from the back of your head orbited completely to meet your eyes. As you turned your head horizontally, you'd see the back of your head in every direction. What would the "smear of heads" look like? And what would it look like when you looked up and down?
I'd love to be able to create a picture of this.
I don't know about standing but here you can visualise falling into two types of black hole :
If you ignore all the reasons this is completely impossible, and assume all the other space around the black hole is free of bright things, this is actually pretty interesting. Your eyes would have to be on the event horizon, and any light that orbits the black hole successfully would have to reflect at an angle nearly exactly tangent to the event horizon. Either way, you likely aren't going to stay there for long, so it would look like a flash of your head as you flew by. As light above the event horizon escapes the black hole the image you see stretches at the top, and as the light emitted underneath the event horizon falls toward the mass the bottom of the image stretches down. The stretching could be so significant you wouldn't recognize the back of your head, or it might not be noticeable.
It would be tangent to the event horizon because the speed of light is constant and orbital radius is a function of speed. If the light were to orbit with an eccentricity greater than 0, the light would necessarily cross the event horizon and never return.
Oh wow! Didn't think of that. I found this: http://en.wikipedia.org/wiki/Photon_sphere Cool stuff. Thanks aerowid.