I’m an engineer, not a physicist, but my understanding is that the ‘spacetime’ around the black hole is bending – this video explains better than I can (try to)
Our current understanding is that it is spacetime that bends. Every object with a mass will bend spacetime but things like stars, black-holes and galaxies will have a very large effect. This can create something called gravitational lens where you can see objects directly behind another object. Of course we are talking very large objects and distances.
Here is an example: http://hubblesite.org/newscenter/archive/releases/1990/20/image/a/
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