Short answer: we don't know.
Longer answer: Albert Einstein's theory of general relativity, which is the theory of gravity that predicts black holes, predicts that there should be a singularity: a location of zero volume, infinite density, and infinite gravitational field strength, at which time literally comes to an end.
In our experience in physics, when a theory predicts singularities, it usually means that the theory is breaking down. Additionally, the Heisenberg uncertainty principle from quantum mechanics flatly states that such singularities are impossible. It could be that quantum mechanics is wrong about this, or that relativity is wrong, or even that both of these theories are wrong. However, both general relativity and quantum mechanics work very well at explaining and predicting the phenomena where they have been tested, so it is impossible to tell how and at what point one or both of them may break down.
"The short answer is, physicists don’t know. A somewhat longer answer is, it depends on whom you ask."
“The event horizon is where the escape speed exceeds the speed of light: you'd have to be going faster than light (which is impossible for any bit of matter) to escape the black hole's gravity. Inside the event horizon is where physics goes crazy. ... A singularity is what all the matter in a black hole gets crushed into.Dec 28, 2016”.
Inside a black hole.
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