Mathematically, they should exist. We have never seen one, only traces of evidence that we think *might* happen near a black hole. Gravitational lensing is due to the proximity of large stars, not black holes. We assume they exist, because it does comfortable things for us like explaining why galaxies exist (supermassive black holes at the center of the galaxy), but we have never observed one. They are an artifact of math, which I believe Steven Hawking has recently come out with a paper making the existence of black holes even more theoretical. I think I have the link below, if not to the article, to an explanation.