Based on the external clock attached to the distant reference frame of the universe, your motion towards the event horizon reaches relativistic speeds once you get within a few percent of the radius of the black hole from its event horizon. As seen by the distant observer, your clock slows down just as though you were boosted to a speed near that of light...which you are in fact! By your clock falling into the hole, it will not take you long to reach the horizon, perhaps only a few seconds, and you may not feel any tidal effects at all if the hole is big enough. So far as I understand the relativistic effects, by the time you are within a micron of the event horizon, the external universe clock (dT) will be ticking at a rate of one of your seconds every:
1 second
dT = ------------------
1/2
( 1 - R/r )
R = horizon radius = 2.7km = 270000 centimeters
r = your distance = R + 1 micron = 270000 + 0.0001
so 1
1 - R/r = (R + 1 micron - R)/(R + 1micron) = ----------------
(1 + R/1micron)
or 1 - R/r = 3.7 x 10^-10
and so dT = 52000 seconds or 14 hours.
Well, at this pace, not a whole lot will seem to happen as you look out at the external universe, but as you get even closer, the time dilation factor increases sharply, and in principle you would not be able to out last the rest of the universe collapsing in a mad rush behind you! The only caviat I can think of is that by the time you reach a distance from the horizon where the dilation factor is big enough to see cosmic evolution, you have reached quantum scales of distance. In your freely-falling frame of reference, quantum indeterminacy puts you in the position of not being able to see this cosmic change very clearly as you pass through the horizon because all the cosmic activity would be collapsed into a span of distances near the horizon, much less than the diameter of an atom. At your speed, all of this cosmic history would pass within a microsecond, and then you are through the horizon.
So far as I know, no one has seriously looked at this problem in detail, although we know that the formal black hole solutions are all 'asymptotic' ones that are only valid as the end-states of the collapse process, which by external clocks, takes an infinite amount of time to achieve. If the external spacetime collapses before then, then clearly, the correct 'black hole' solutions are not the asymptotic ones everyone is always talking about.
Copyright 1997 Dr. Sten Odenwald
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