Checkboard Analysis

[Aron Wall]

squark wrote:

> In article <39078381...@wall.org>,
> Aron Wall wrote:
>
> > [squark wrote:]
>
> > > Yes, and of-course I get them to collide before the white hole
> > > turns black too.
>
> > > Sorry. You can't do that. Each falls into the other as a black
> > > hole. It was a little bit misleading for me to say that a white
> > > hole turns into a black hole after it emits all the matter it's
> > > going to emit. From the point of view of an external observer,
> the
> > > hole can absorb objects even before it quits emitting objects.
>
> Okay, this seems wrong to me. Look at the Penrose diagram of an
> eternal black-hole. Nothing can fall into the white-hole
> part, that's for sure.
> ...
> Okay, I got the idea. I see why the two views are equivalent (related
> by a diffeomorphism). But I still disagree on the "the hole
> can absorb objects even before it quits emitting objects" part.
>
> Regards, squark.

Let me restate a sentence I wrote previously with a little change in
emphasis:

****FROM THE POINT OF VIEW OF AN EXTERNAL OBSERVER**** the hole can
absorb objects even before it quits emitting objects.

Nothing falls into the white hole event horizon. And all points on the
black hole horizon are causally in the future of all points in the white
hole horizon. BUT, stand just outside the hole and watch. Say you are
holding an Etruscan vase. You let go and it falls down and disappears
from sight. "This must be a black hole already," you say. "After all it
just ate the vase. But then, all of a sudden, this sofa hurls out of
the hole straight toward you, colliding with your body with great
force. As you float away in comfort, you say "Gee, its still a white
hole. And now that I look at it some more, I see that the thing is
glowing somewhat. That's odd, I never would have believed it, but the
white hole emitted something!"

Confused? Perhaps you'd like to see the entire script for the play,
four events in causal sequence from first to last:

A. The sofa passes through the white hole event horizon.
B. The Etruscan vase, falling into the hole, disappears from sight.
C. The sofa, falling out of the hole, comes into sight.
D. The Etruscan vase passes through the black hole event horizon.

The stuff with the event horizons happens in the order you expect, but
the "coming into/out of view" events happen in the reverse order from
the way that you expect (though they could have happened the other
way). Now you might say to this, "I don't care about what I *see*
happening, I care about what actually happens. The fact that the sofa
looks like it comes out after the vase falls in is just an optical
illusion." Now, there is nothing really *wrong* with this attitude.
You can use Kruscal-like or Penrose-like co-ordinates only, and you will
get the right answers. But I contend that what is observed from outside
is the more natural viewpoint, especially when you consider collisions
of multiple holes. From the Kruscal point of view the event horizon
starts out white and spherical, it shrinks in size, and then is replaced
by an expanding black hole. But if you don't care about what happens
within the horizon, the hole can be more usefully described as a sphere
of constant radius with time translation symmetry into which things can
both fall in, and out. And from this perspective, events B and C are
more important than events A and D.

Aron Wall