Also punching above my weight class here: isn't observation a function of time as well though, so a local observer would notice no difference in their perception of the passage of time? It's only across distance that the perception of time would change per relativity, so obseevation of self would remain the same while observation of distant objects would appear to experience time faster, while an outside observer would perceive their own time constant and that of the infalling observer to slow through time.