From: anderson@fermi.phys.ualberta.ca (Warren G. Anderson)
Subject: Re: On the formation of black holes
Organization: University Of Alberta, Edmonton Canada
Date: Mon, 27 Jul 1992 22:11:20 GMT

In article <84510@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P  
Wiener) writes:
> In article <1992Jul24.204636.13806@kakwa.ucs.ualberta.ca>, anderson@fermi  
(Warren G. Anderson) writes:
> I've only been justifying "black", and the S&S figure was a wrong refer-
> ence for my point.  My apologies.  I have a copy of MTW in front of me now,
> so all my references should now be accurate, and I won't just hand-wave my
> thoughts here.  An outgoing null cone--the one I've been thinking of--is
> shown on page 830.

The diagram for outgoing Eddington-Finkelstein coordinates on page 830 shows 
the world-line for an infalling photon. Note that the photon does not reach
the horizon before U = infinity. Note also that the worldline of an infalling
time-like test particle will not cross the horizon before the photons. 
In short, in we see in Eddington-Finkelstein coordinates that the infalling 
test particle passes through *every* outgoing null surface in the spacetime. 
Thus, there will never be a *last* outgoing null surface that the test particle
can emit on; every outgoing null surface that a stationary observer passes
through can contain an emission from the test particle. 

> Page 830 shows what is happening in outgoing E-F coordinates.  You'll see
> the finiteness I've been talking about very explicitly, very geometrically.

Only if the particle reaches the horizon at a finite retarded time (U-coord.)
Since it doesn't, there is no cutoff.

> Wrong figure, my fault.  Surely you can see the outgoing cone anyway--much
> like fig 34.1 (for neutron stars), or the figure on page 830?  Any photon
> emitted by the infalling star is external to this outgoing cone.  So when
> a stationary external observer--one whose world line is parallel to the
> singularity--crosses the cone, he no longer sees the infalling star.  The
> hole is now completely black.  No details about how matter emits photons
> are used here, hence my claim that this is a purely geometric argument.

The stationary observer does not cross this cone in finite proper time.

> Look at Box 31.2, pp 828-831.  Follow the stationary observer at r=5M in
> the figure on page 830: he intersects the outgoing null cone in finite
> proper time.  This is done in outgoing Eddington-Finkelstein coordinates.
> Now, outgoing E-F describe infall pathologically--perhaps that r=5M is a
> different coordinate illusion that I've fallen victim too, and does not
> represent something stationary after all?  It could be, but I don't see it.

No, r=5M is stationary, it's just that the outgoing cone is not drawn at the
point where a test particle could cross r=2M in this diagram.

> They explicitly say that an arbitrary low amount of possible radiation
> omitted holds even in the continuum approximation--discretization of
> emission only accelerates this part of the process.  But overall I've
> been giving you the wrong references for the details I've had in mind.
> Sorry.

I agree, the classical field can be made arbitrarily but finitely small
by having the classical observer look at a suuficiently great proper time.
However, as long as the field is classical, I maintain that it can affect the
stationary observer for an infinite amount of the observers proper time before
it becomes infinitesimal.

--
########################## _`|'_ ##############################################
##  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)      ##