From: jonathan@iron.astro.indiana.edu
In article , I wrote:
> In (crude, but still useful) ASCII-art, we thus have
>
> t O marks the dust cloud
> /|\
> * * marks the singularity
> *
> *
> t=Z *
> OO
> OOOOO
> OOOOOOOO
> OOOOOOOOOOO
> OOOOOOOOOOOOO
> OOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOOOO
> t=0 OOOOOOOOOOOOOOOOOOOOOO----> r
>
> (This is essentially the Misner, Thorne, & Wheeler figure 32.1c to
> which I referred earlier in this thread.)
>
> [In my diagram the "*" points mark a singularity. These points aren't
> actually in our differential manifold, and the metric isn't well-defined
> there.]
Correction: the singularity typically forms a bit before t=Z, so my
diagram should have looked more like this:
t O marks the dust cloud
/|\
* * marks the singularity
*
*
t=Z *
*O
*OOOO
*OOOOOOO
*OOOOOOOOOO
*OOOOOOOOOOOO
OOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOO
t=0 OOOOOOOOOOOOOOOOOOOOOO----> r
Later in article , I wrote:
> At $t > X$ the EH will expand outwards at the (local) speed of light,
> eventually becoming $r = 2M$ once all the dust has fallen through the
> EH. Let's call the time at which the last of the dust falls through
> the EH $t = Y$. Our ASCII-art picture is now this:
>
> t O marks the dust cloud
> /|\
> * : * marks the singularity
> * :
> * : : marks the event horizon
> t=Z * : (which is also the trajectory
> OO : of a light flash emitted at
> OOOOO : the event $(t,r) = (X,0)$)
> t=Y OOOOOOO:
> OOOOOO:OOOO
> OOOOO:OOOOOOO
> OOO:OOOOOOOOOOO
> t=X :OOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOOO
> OOOOOOOOOOOOOOOOOOOOOO
> t=0 OOOOOOOOOOOOOOOOOOOOOO----> r
> | |
> r=0 r=2M
Making the same correction to my 2nd diagram suggests that it should
have looked more like this:
t O marks the dust cloud
/|\
* : * marks the singularity
* :
* : : marks the event horizon
t=Z * : (which is also the trajectory
*O : of a light flash emitted at
*OOOO : the event $(t,r) = (X,0)$)
t=Y *OOOOOO:
*OOOOO:OOOO
*OOOO:OOOOOOO
OOO:OOOOOOOOOOO
t=X :OOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOO
t=0 OOOOOOOOOOOOOOOOOOOOOO----> r
| |
r=0 r=2M
ciao,
--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
currently visiting Max-Plack-Institute fuer Gravitationsphysik
(Albert-Einstein-Institut), Potsdam-Golm, Germany
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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