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I mostly agree with this. But I want to point out that the concept of
the matter inside the event horizon as being characterized as "infalling"
is misleading. An observer *outside* the horizon *does* understand any
matter falling through the horizon (even if it may take an infinite time
for it to *appear* to do so) to be legitimately called 'infalling'.
But once the matter is inside the event horizon it is *not* falling
through space in time toward a central singularity in space. Rather, the
matter finds itself in a region of spacetime where the space itself is
contracting.