From: anderson@fermi.phys.ualberta.ca (Warren G. Anderson)
Subject: Re: On the formation of black holes
Organization: University Of Alberta, Edmonton Canada
Date: Thu, 23 Jul 1992 17:58:38 GMT

In article <84062@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P  
Wiener) writes:
> In article <1992Jul21.194850.25821@kakwa.ucs.ualberta.ca>, anderson@fermi  
(Warren G. Anderson) writes:
> >In article <83854@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P  
> >Wiener) writes:
> 
>>> That the external observer sees infalling material disappear in a finite
>>> time, contrary to what was believed three decades ago, because people
>>> didn't yet understand the difference between time and t.
> 
>>In fact, this is not true for a classical source, at least, not if 
>>"disappear" means "no emissions can reach a stationay observer".
> 
> What are you talking about?  An emission that takes a detour to another
> planet first and then comes back?  When physicists were confused about
> "frozen stars" hovering above the event horizon, they thought they were
> talking about an essential phenomenon involving time, not mirror tricks.

Look, it's simple. If a stationary external observer observes a radially
infalling test particle emitting classical radiation she will see emissions
from that particle for an inifinite proper time. No planets, mirrors, or 
anything else. The unquantized emissions fall of rapidly, but there will
always be an emission.
> 
> >I finally got around to looking in the suggested section of MTW.
> 
> Thank you!  I'll repeat that for all of you: MTW, Chap 33.  Glorious and
> amazingly clear.
> 
> >								  I guess I
> >misunderstood what you were saying. What you say above is true. However,
> >the stationary observer never does see anything cross the event horizon
> >(which is what I was saying).
> 
> Well of course not.  We've been both saying that, but you were trying,
> for some reason, to understand this in a Penrose diagram.
> 
> >			       It's simply that the intensity fall off due
> >to the space-time curvature is so rapid that 'virtually' nothing 
> >escaping from a test particle close enough to the event horizon reaches
> >a stationary observer.
> 
> This is a separate issue.  The geometry of collapse alone suffices to
> establish a cone of last influence. 

You seem confused as to what the cone of last influence represensts. It is
not the last point at which the infalling particle has an influence on an 
external observer, but rather locus of points at which an external observer
can last influence the infalling particle. That is why it is an ingoing
null hypersurface, rahter than outgoing. What the observer sees from the
infalling particle has nothing to do with the surface of last influence.
 
> Actually, geometry alone would say
> that you could see that instantaneous moment of crossing, but I don't
> think such notions are well-defined physically.

No it doesn't. Despite your protests, the Penrose diagram does indeed
contain all the necessary information to understand the causal relationships
between different test particles in a spherically symmetric space-time. It
is clear from the Schwarzschild diagram that emissions will reach the 
stationary observer for an infinite proper time.
> 
> >		        Why didn't you just say this instead of saying
> >that my argument using Penrose diagrams was going awry because I was
> >using Schwarzschild time and such?
> 
> Uh, I kept saying over and over again that S-time was just a coordinate,
> and not to be taken seriously without careful interpretation.  If it gets
> through on the fifth try, great!

Either you are not reading my messages very carefully or you are being
belligerent. I never brought S-time into this at all, you did. All I'm
trying to figure out is why?
 
> >				    In the end, it turns out we are both
> >right, just talking about slightly different things. 
> 
> Yes.  My prejudice is for the primary geometrical explanation.  The
> physical mechanisms of near-horizon emission play a supporting role.

There is no geometrical explanation. The infalling test particle (if it
emits classical fields) can influence a stationary observer for an infinite
observer proper time. There is no geometric barrier to this. I think maybe
*you* had better have another look at MTW Ch. 33.

--
########################## _`|'_ ##############################################
##  Warren G. Anderson     |o o| "... for its truth does not matter, and is  ##
##  Dept. of Physics       ( ^ )  unimaginable." -J. Ashbery, The New Spirit ##
##  University of Alberta  /\-/\      (anderson@fermi.phys.ualberta.ca)      ##
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