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Jonathan Scott said:The mathematics of GR extends beyond the event horizon, and says that the shape of space-time is such that there are no possible paths forward in time which stay in one place. Every possible path ends up in the singularity after a limited time.
I find it really helpful to use Penrose diagrams when thinking about this kind of thing. My book Relativity for Poets has a nonmathematical introduction to Penrose diagrams in section 11.5.