From: anderson@fermi.phys.ualberta.ca (Warren G. Anderson)
Subject: Re: On the formation of black holes
Organization: University Of Alberta, Edmonton Canada
Date: Fri, 24 Jul 1992 20:46:36 GMT

In article <84249@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P  
Wiener) writes:
> In article <1992Jul23.175838.6925@kakwa.ucs.ualberta.ca>, anderson@fermi  
(Warren G. Anderson) writes:
> >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.
> 
> This is simply and utterly false.  The external observer sees the black
> hole form in finite proper time, and for purely geometric reasons.

Just because you keep saying this doesn't make it so.
 
> >> 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.
> 
> Those are two different notions.  I am speaking about the former.  I'm
> willing to believe that people use the term "cone of last influence" for
> either, but I'm only using it for the former.

MTW does not speak about the former but the latter, and since that is the
only place I have encountered the notion (at your behest) I took my 
definition from there. Are you using a different definition than MTW?

["Does so", "Does not" section deleted :-)].
 
> >It is clear from the Schwarzschild diagram that emissions will reach the 
> >stationary observer for an infinite proper time.
> 
> Wrong.  The infalling object hits the event horizon at some event, and
> from there is a cone (at 45 degree for c=1) reaching out from that.  Where
> it crosses the observer's worldline, that's it: no more influence from the
> object falling in (except via mirrors, of course).

That is only true in coordinates in which null geodesics extend along 45
degree lines, such as the u,v Kruskal coordinates of a Penrose diagram, 
in which u=const and v=const are radial null coordinates. On such a 
patch it is clear that the point at which a stationary observer reaches the
last null ray is future infinity (that's proper time).
  
> >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.
> 
> There is a geometric barrier, pure and simple.  Look at MTW Fig 33.1 and the
> cone heading out.  That's what it boils down to.  The quantum effects merely
> accelerate this process.

I am looking at that diagram right now. It shows "The surface of last influence
.. an ingoing null surfact that intersects the horizon in coincidence with
the surface of the collapsing star. After an external observer, moving
forward in time, has passed through the surface of last influence, he can
not interact with and influence the star before it plunges through the
horizon." MTW p873.

This is almost misleadingly worded. the "and" must be interpreted in the
strict sense for this sentence to be meaningful. However, clearly 
from the picture and the surrounding discussion in this chapter, MTW do
not mean (and could not correctly say) that the star can not interact with
and influence an esternal observer past this point. 

I am afraid that one of us is interpreting MTW incorrectly. I have gone
over this section a couple times now at your insistence, and I am almost
positive it is you who needs to re-evaluate what they are saying. However,
I can think of no way to convince you that you are wrong. What would it take?
When was the last time you read through the discussion between Sagredus and
Salvatius? Unless you can offer me something more than you have already,
I'm afraid that I'll have to conclude that you are wrong and incapable (or
unwilling) to understand why. 
--
########################## _`|'_ ##############################################
##  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)      ##