Steve Price, MD:
> Jon Perez Laraudogoitia:
> "An example of such a spacetime is an electrically charged black
> hole (the Reissner-Nordstrom spacetime). A well known property of
> black holes is that, in the view of those who remain outside,
> unfortunates who fall in appear to freeze in time as they approach
> the event horizon of the black hole. Indeed those who remain
> outside could spend an infinite lifetime with the unfortunate who
> fell in frozen near the event horizon. If we just redescribe this
> process from the point of view of the observer who does fall in to
> the black hole, we discover that we have a bifurcated supertask. The
> observer falling in perceives no slowing down of time in his own
> processes. He sees himself reaching the event horizon quite
> quickly. But if he looks back at those who remain behind, he sees
> their processes sped up indefinitely. By the time he reaches the
> event horizon, those who remain outside will have completed infinite
> proper time on their world-lines."
This is completely wrong! Outside observers do indeed see the faller
asymptotically approach the horizon, with falling wristwatches
asymptotically approaching a certain specific time. But that does not
mean the infaller sees an infinite speedup looking out! The photons
following the infaller are equally slowed down, and those are all he
can see.
If you study the geometry of a black hole (most clearly in
Kruskal-Szekeres coordinates, found in a diagram in Wheeler, Misner
and Throne's "Gravitation", or (too coarsely) in
http://casa.colorado.edu/~ajsh/schwm.html#kruskal ), you will see that
an observer infalling into a black hole receives only a small finite
number of signals from any regularly ticking clock outside the black
hole, even as the observer passes through the event horizon and
continues on through to be eaten by the singularity.
Note that if the faller really did see the external universe speed up
infinitely, then the light he saw at the last moment would have been
blue-shifted infinitely, an infinite amount of it compressed into a
finite time, instantly incinerating the faller, then his elementary
particles, and then their constituents! Yow!
Received on Fri Jul 16 1999 - 19:00:34 PDT