Time and space work exactly the same inside the black hole as outside, they just swap places. One dimension that was spacelike is bent into becoming timelike. Closer to the center becomes further in the future, and outside the event horizon becomes part of the past. The singularity at the center of the black hole is now the literal end of time. Nothing exists past the end of time; you hit that singularity and you cease to exist.
From the outside, all that we can detect is the mass of the black hole. Or rather, all we can detect is some gravity pulling us in, as if there were mass inside. Einstein proved that all gravity is just the curvature of spacetime. Your body is bending the fabric of spacetime right now!¹ When you dive into a black hole, the curvature you are causing is added to that of the black hole, so that the black hole grows exactly as if your mass still existed inside of it. But really you ceased to exist when you hit the end of time at the singularity.
But of course that is how we _used_ to think of it, up until a decade or two ago. As Susskind would say, ER=EPR. Spatial connectivity (which Einstein and Rosen wrote a paper about) is exactly the same thing as quantum entanglement (which Einstein, Podolsky, and Rosen wrote a completely different paper about in the same year). I won’t try to recapitulate one of his lectures (since you can just watch one; see <https://www.youtube.com/watch?v=31fVea8_OAw> for a recent example, but there are others), but the result is that the spacetime inside the black hole grows without bound, and you never actually reach the end of time. You cannot go back, but neither do you go splat. The matter that was once a star is somewhere ahead of you in that growing region of spacetime, forever in your future.
¹ Note all possible “yo mamma” jokes for future reference.
Let me rephrase: The time we measure with our clocks from the outside doesn't apply inside of black holes. There is no way to say whether any singularity has ever formed or ever will form even according to the math, since time inside of them isn't the kind of time we can measure from the outside.
If you go inside of it the math says that now your clock inside of the black hole can still function, but that also means you are no longer connected to time outside of the black hole, so you can't say whether anything actually happens inside of them from our perspective, all the math says is what it would be like for someone inside.
You need to make extra assumptions about what it means to have a disconnected time reference frame to say anything.
Time and space work exactly the same inside the black hole as outside, they just swap places. One dimension that was spacelike is bent into becoming timelike. Closer to the center becomes further in the future, and outside the event horizon becomes part of the past. The singularity at the center of the black hole is now the literal end of time. Nothing exists past the end of time; you hit that singularity and you cease to exist.
From the outside, all that we can detect is the mass of the black hole. Or rather, all we can detect is some gravity pulling us in, as if there were mass inside. Einstein proved that all gravity is just the curvature of spacetime. Your body is bending the fabric of spacetime right now!¹ When you dive into a black hole, the curvature you are causing is added to that of the black hole, so that the black hole grows exactly as if your mass still existed inside of it. But really you ceased to exist when you hit the end of time at the singularity.
But of course that is how we _used_ to think of it, up until a decade or two ago. As Susskind would say, ER=EPR. Spatial connectivity (which Einstein and Rosen wrote a paper about) is exactly the same thing as quantum entanglement (which Einstein, Podolsky, and Rosen wrote a completely different paper about in the same year). I won’t try to recapitulate one of his lectures (since you can just watch one; see <https://www.youtube.com/watch?v=31fVea8_OAw> for a recent example, but there are others), but the result is that the spacetime inside the black hole grows without bound, and you never actually reach the end of time. You cannot go back, but neither do you go splat. The matter that was once a star is somewhere ahead of you in that growing region of spacetime, forever in your future.
¹ Note all possible “yo mamma” jokes for future reference.