Are black holes in a sense transparent? Meaning, they don't 'hide' any stars that happen to be 'behind' them?
A regular object obviously blocks a point source of light emanating from 'behind' it. Meaning it creates an area of space photons cannot get to us from. But a massive object curves space, and so via gravitational lensing we can sometimes see distant stars that are 'behind' other stars (by behind I mean that if the star in the middle would suddenly vanish, the trajectory of photons traveling from the distant star to Earth would have passed through the volume now occupied by the middle star).
My thinking, is that black holes curve space so much, that from ANY source of light outside it, light has a trajectory to reach us on Earth (assuming of course no other object blocks it on its way).
The reasoning for this is: Suppose we draw the straight line between us and the light source (as if the black hole wasn't there at all). Photons from our light source crossing the event horizon would obviously 'fall' inside. A photon in theory traveling exactly tangent to the event horizon would in a sense go 'into orbit' around the black hole (obviously there is no such thing, because the black hole isn't perfectly spherical, and there are quantum effects and so forth. But I'm focusing on the geometry), crossing our straight line exactly at the intersection of our line and the event horizon. Any photon passing near the event horizon, but a bit farther, would follow a curve that intersects our line a little farther from the event horizon. Continuing this, there would be at last be a photon that would exactly curve our way.
