Some physicists feel the question of what happens in a black hole is academic or even theological. But at stake are the future rules of physics.
Black Holes are possibly the most interesting objects in the universe, for their extreme distortion of spacetime and their ability to do so while remaining extremely fundamental entities (almost like elementary particles), fully described by three parameters only: their mass $M$, their charge and their angular momentum (spin). This allows them to be described quite accurately by the equations of General Relativity.
They are discussed in more detail in Lecture 23 of my Modern Physics course of the Wolverhampton Lectures of Physics as well as in my Nobel Prize Lecture for 2020.
Interstellar is a movie of note that attempts to tackle the subject.
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