From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Sep 12 2003 - 23:33:23 MDT
Brian Atkins quotes
> The black hole survival guide
> New Scientist vol 179 issue 2411 - 06 September 2003, page 26
>
> Falling into a black hole need not spell certain doom. Marcus Chown
> looks forward to the ultimate thrill ride
...
> Fantastic voyage
>
> Immediately ahead of you lies the event horizon, the point of no return
> for in-falling light and matter. Here time appears to slow to a
> standstill, so your friends see your gradually fading image frozen in
> space forever. The truth (for you, anyway) is that you have long gone
> over the event horizon and are falling towards the singularity, the
> point with infinite density.
What is this inter-subjectivity of the equivalence of time,
anyway? Isn't this much like pointing to a frozen cryonics
patient and expostulating to others nearby, "the truth for
our friend, here, is that he has long gone past the point
where he was reanimated; the several hours of our time since
his deanimation corresponds for him (in his nearly frozen
frame) of at least a couple of hours after his revival."
The notion that we observe a black hole for hundreds of years
years and that meanwhile we can assert "he (our friend) has
long gone over the event horizon" may be ultimately arising
from such a feeling of temporal intersubjectivity.
Before these remarks are taken as those of a crank, please
appreciate the following. The first 5 are for sure true in
classical GR theory pertaining to black holes:
1. Photon trajectories into a stationary black hole are
symmetrical, in that a photon would take as long to
reach a tiny mirror suspended just above the event
horizon as it would take to make the return trip
2. There is no latest time at which external observers
may receive such a photon, which takes this symmetrical
journey, nor receive a photon emitted by an infalling
astronaut
3. the (external) time required for such a complete round
trip is approximately ln(1/(r-2M)), where 2M is the
radius of the black hole, and r is the position of the
mirror. (This expression obviously diverges as r
becomes very close to the event horizon.)
4. Though one has to be very careful when attempting to
define simultaneity at remote distances, as Wheeler
and Ciufolini write on page 100 of "Gravitation and
Inertia", 1995,
Furthermore, if spacetime is static we can find a
coordinate system where the metric is time independent,
therefore the coordinate time T required for an electro-
magnetic signal to go from a coordinate point A to any
other coordinate point B is the same as the coordinate
time T for the signal to return from B to A. Therefore,
one can consistently define *simultaneity* on the manifold
between any two points using light signals between them.
5. The Schwarzschild time coordinate of the event horizon is
infinite (though of course that would mean nothing to an
astronaut using his own infalling coordinate system).
This infinity is removed by transforming to the Kruskal-
Szekeres coordinates (see pages 833 through 835 of
"Gravitation" by Wheeler et al.). However, events that
occur in one coordinate system occur in all coordinate
systems, and all finite values of t in Schwarzschild
coordinates correspond to real positions of the infalling
astronaut, and all such positions (for finite t) are
*outside* the event horizons.
6. Therefore, if the black hole exists for only finitely long,
(as in Hawking's theories), it becomes less than clear that
the time-retarded astronaut crosses the event horizon before
the black hole evaporates.
7. At the conclusion of a lengthy debate I held on this topic
on sci.physics.relativity, a Berlin physicist Ilja Schmelzer
wrote on 23 August 2000 in my thread "Why is the frozen
star concept passe", evidently in my defense,
"It radiates away in finite external Schwarzschild time.
Are you sure that it succeeds to form a horizon before
radiating away? Hint: go back in time from the event
where the outside observers observe late Hawking radiation
to the black hole, and ask where it meets the infalling
observer.
"That the black hole evaporates completely before even
forming a horizon is not crackpot nonsense, but a scenario
proposed by Gerlach, PRD 14(6), 1976."
There were no substantive rejoinders to Schmelzer's post, so
long as I remained in the discussion (but see below).
So I stand unconvinced that the event horizons can be said to
have finished forming anywhere. The black hole FAQ at
http://antwrp.gsfc.nasa.gov/htmltest/gifcity/bh_pub_faq.html
helps a little, but not much, as it seems at crucial points to
invoke this same suspect temporal intersubjectivity.
Evidently, the discussion was going on about a month after I left:
http://www.lns.cornell.edu/spr/2000-10/msg0029139.html
Lee Corbin
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