According to a talk I heard today, black holes don't have a singularity in the middle, but instead are covered in quantum hair.
If you squeeze mass into a smaller and smaller volume (for instance when a big star collapses) the gravitational field around it gets stronger and stronger. At some point it becomes so strong that not even light can escape, and you have a black hole.
Until today, the understanding I had of black holes was as a spherical "event horizon" with a singularity at the centre.
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