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Black hole vs Black hole 
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#19
Feb2713, 03:22 AM

P: 887

It is possible to station an observer at a position at respect to the black hole if they were very far away; this observer will *see things slow down as they fall towards the black hole*. Of course, the falling things will also *exponentially redshift and dim away* which makes them visually "look" like they are falling in. Since light is actually discrete, the last photon that leaves will reach your eyes in a finite and quite short time, and then there's no more images; that's why you can "see" things fall through black holes. This is because the coordinate called "t", which corresponds to proper time in your faraway frame, does not necessarily correspond to proper time in another frame. If YOU were the one falling in, for a black hole with a large mass, you won't even *know* when you fell through the event horizon, because your proper time τ does not correspond to the time outside t. 


#20
Feb2713, 06:25 AM

PF Gold
P: 171

http://math.ucr.edu/home/baez/physic...s/fall_in.html
You can read more in the second section of this reference. But to reply directly, if the infalling object is not a mathematical point, but actually has a size, it will not reach infinite speed before it falls in, and so time wont "stop". Even a point only reaches light speed at the exact same instant it "falls in". Also even if time "stops" for the infalling object, it does not stop for the outgoing event horizon. Second point; A black hole space time (with one dimension suppressed) resembles a pencil. I think you should ignore the point of the pencil and concentrate on the cylindrical barrel. That is where the conventional description applies. Further, if you include quantum effects, the object can "tunnel in". Your original math is correct as far as it goes, but it doesn't capture the whole picture. 


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