**From:** Lee Corbin (*lcorbin@tsoft.com*)

**Date:** Fri Sep 12 2003 - 23:33:23 MDT

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Brian Atkins quotes

*> The black hole survival guide
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*> New Scientist vol 179 issue 2411 - 06 September 2003, page 26
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*>
*

*> Falling into a black hole need not spell certain doom. Marcus Chown
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*> looks forward to the ultimate thrill ride
*

...

*> Fantastic voyage
*

*>
*

*> Immediately ahead of you lies the event horizon, the point of no return
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*> for in-falling light and matter. Here time appears to slow to a
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*> standstill, so your friends see your gradually fading image frozen in
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*> space forever. The truth (for you, anyway) is that you have long gone
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*> over the event horizon and are falling towards the singularity, the
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*> 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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