From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.astro
Subject: Re: On the formation of black holes
Date: 27 Jul 92 18:57:33 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: anderson@fermi.phys.ualberta.ca (Warren G. Anderson)

In article <1992Jul24.204636.13806@kakwa.ucs.ualberta.ca>, anderson@fermi (Warren G. Anderson) writes:
>> 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?

Yes.  We were talking about a stationary external observer, so only the
outgoing notion is relevant.  MTW is justifying both "black" and "hole".
Their figure 33.1 with the incoming cone represents a geometric boundary
outside of which an external observer cannot swoop in and scoop up star
stuff, and hence the use of the term "hole" is justified.

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.

>> >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).

Something does not parse in the above, since you start by agreeing that I
am speaking truth and then you conclude that I am speaking falsity.  As it
is, I've pointed out before, when you first raised this particular issue,
that even the Kruskal coordinates are misleading here.  Just like the
original confusion was historically caused by not distinguishing the
Schwarzschild coordinate t from external observer time, so is this one.

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.

>> >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.

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.

If you want to include some physical effects, like photon speed is less
than c based on the medium, then draw an outgoing cone for v=.5 starting
at the sphere where the infalling star crosses the radius corresponding
to escape velocity c/2, and the same argument will apply.  I'm excluding
light echos and all other ways to delay photons as not being normal usage
regarding the notion of potentially seeing the infalling matter for a black
hole.  We all agree that you could watch the star on instant replay forever.

>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. 

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.

>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.

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.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)