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To be honest I really can't get past what "the end of time" even means.

If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?

Time is necessary for change, not existence.

Time is change that happens in a continuous manner. It’s still possible to conceive of change happening in an unordered unpredictable way that is not like the smooth ordered time that we experience.

In a gravitational singularity spacetime breaks down. You could argue that time stops, but it’s also valid to argue that causality breaks down and we can no longer make any predictions about the future. Just because we don’t have a theory describing what could happen, doesn’t rule out that something could happen.

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