existence beyond event horison
Chris Hillman
> How does event horizon emerge and behave when a star is collapsing
> into a black hole? I suppose the horizon first emerges in the center
> of the star. Then it expands up to stationary Schwarzschild radius
> while the star's matter falls down and hides under the growing radius.
You might want to take a look at the discussion in Frolov & Novikov, Black
Hole Physics, Kluwer, 1998. It is essential to understand that the
definition of an -event- horizon is -global-, i.e. depends on the entire
subsequent history.
> What is destiny of the star's matter? I think it is not quite
> correctly to say that there is "very dense matter within a black hole"
> because it's impossible to determine the fact experimentally. Yes,
> black hole has its mass. The mass is measurable. But we don't know
> which matter is "within" the black hole.
The trouble with this is that you now have the burden of explaining why
(so far as we can tell!) gtr very accurately predicts dynamics just
outside the event horizon of real black holes (specific astrophysical
objects which have been observed for a decade or more), but then
(according to your viewpoint) suddenly breaks down just at the horizon.
This is particularly difficult because according to gtr there is nothing
"locally" special about this horizon.
(In the literature on realistic models of black hole interiors, there has
been much talk of Cauchy horizons inside this event horizon which might
feature caustics, i.e. a locally measureable physical effect, but this
does not contradict anything I have said above. See for instance papers
by Israel and others at http://prola.aps.org/search.html.)
> No one real world line enters into this region.
If you are talking about gtr, that is unequivocally untrue. See the
discussion of Lemaitre, Kruskal-Szekeres, Penrose, or Novikov coordinates.
These are all fairly intuitive, but the Lemaitre coordinates are
mathematically the easiest to derive, and the KS coordinates are not much
harder and have the benefit of covering the maximal completion, which the
Lemaitre coordinates do not. However, the Lemaitre coordinates are
perfectly adequate for discussion of radial infall, and should help you to
understand that gtr predicts that if you drop your watch near a black
hole, it can drop through the horizon in finite time. Look for a post of
mine on sci.physics.relativity where I gave a detailed derivation of the
transformation to the Lemaitre coordinates, or see books like MTW or
Frolov & Novikov or Stephani.
> So we cannot even say "black hole's inside exists" in present time.
"Present time" is a tricky notion in gtr! To see why, look at the
discussion on books like Hawking & Ellis, The Large Scale Structure of
Space Time, Cambridge University Press, 1973 (just reprinted) or Frolov &
Novikov.
I see I am more or less repeating what John Baez and Toby Bartels said,
but I hope that the references I provided will prove useful.
Chris Hillman
Eugeny Kornienko
>> No one real world line enters into this region. So we cannot even
>> say "black hole's inside exists" in present time.
> the laws of physics (general relativity) allow you to postulate the
> inside of a black hole, even though no observer whose word reaches
> you sees it.
Sure, worldlines (and free falling bodies) reach singularity, and
matter exists there. We only don't know the form of that matter.
Perhaps I was unclear. I meant that external observer, which is not
free falling onto the black hole, cannot observe external worldlines
penetrating into event horizon.
We cannot resolve any matter in the "singularity" where all mass of
black hole is concentrated. So the matter within black hole (= beneath
its event horizon) (= in the point of singularity) exists rather
theoretically than physically.
There is more abstract example of such "non-physical existence".
General relativity allows strictly close space-time. If the theory is
valid to universe on the whole then any amount of close universes,
which obey general relativity, may exist. They don't connect and don't
interact to each other. It's logically wrong to say that such
universes exist "now" or "forever". Unlike black holes they are not
connected to us by worldlines at all. They exist only theoretically,
in principle.
What is interesting to me here - current physical theory allows
objects that are not measurable and are not observable in principle.
Let a very reliable physical theory predicts such an object. Is it
correct to say that such object exists?
I think, if we trust the theory, we are forced to accept that such
non-measurable object exists but the existence doesn't matter to other
"physically" existing objects.
Eugeny Kornienko
Forsaken
>>correctly to say that there is "very dense matter within a black hole"
>>because it's impossible to determine the fact experimentally. Yes,
>>black hole has its mass. The mass is measurable. But we don't know
>>into this region. So we cannot even say "black hole's inside exists"
>>in present time.
This is the purely GR solution yes. And one can prove using GR that all the
matter collapses to a point. However, the Heisenburg Uncertainty Principle
(which applies here) would suggest that since we supposedly know the
location of all the matter exactly (hence a point) we cannot know the
momentum of that point. It would thus be possible to quantum mechanically
tunnel out of the black hole! Or what's worse: we would not know where the
darn thing was going!
The bottom line is this, QM indicates that the point solution is probably
not right. That on some scale (Plank scale) quantum effects and gravity
mix. On this scale plain old GR won't do and you won't get the right
answers using it. The true density of the black hole is not really known
since we don't currently have a working and experimentally verified model of
quantum gravity.
>
>>Also present time may confuse when we speak about matter
>>beyond external event horizon in universe. The matter exists in
>>principle, theoretically, not "physically". It isn't measurable in
>>principle.
I would say that in fact the matter is measurable. Hawking showed the black
holes to have entropy. We see matter "leaking out".
Toby Bartels
>Toby Bartels <to...@ugcs.caltech.edu> wrote:
>>The laws of physics (general relativity) allow you to postulate the
>>inside of a black hole, even though no observer whose word reaches
>>you sees it.
>Sure, worldlines (and free falling bodies) reach singularity, and
>matter exists there. We only don't know the form of that matter.
>Perhaps I was unclear. I meant that external observer, which is not
>free falling onto the black hole, cannot observe external worldlines
>penetrating into event horizon.
If that's what you mean by
>>>No one real world line enters into this region.
then that's all right. However, it still doesn't follow that
>>>So we cannot even say "black hole's inside exists" in present time.
since an unobserved worldline nevertheless enters the inside.
(If it's "present time" that bothers you,
you can still choose coordinates such that
the inside of the hole exists at the present time;
you don't have to use Schwarzschild coordinates.)
>We cannot resolve any matter in the "singularity" where all mass of
>black hole is concentrated. So the matter within black hole (= beneath
>its event horizon) (= in the point of singularity) exists rather
>theoretically than physically.
The singularity itself is different.
I think the problems with the singularity will only be resolved
with a quantum theory of gravity.
But beneath the event horizion does *not* equal at the singularity!
There's quite a bit of spacetime between the horizon and the singularity.
>There is more abstract example of such "non-physical existence".
>General relativity allows strictly close space-time. If the theory is
>valid to universe on the whole then any amount of close universes,
>which obey general relativity, may exist. They don't connect and don't
>interact to each other. It's logically wrong to say that such
>universes exist "now" or "forever". Unlike black holes they are not
>connected to us by worldlines at all. They exist only theoretically,
>in principle.
Disconnected universes are different from insides of black holes.
Though both are unobservable by us,
GTR does not *require* the existence of disconnected universes,
while it does require the existence of black hole insides
(based on what we do observe).
Thus, Ockham would have us believe in the latter but not the former
(at least not on the basis of reason alone).
>What is interesting to me here - current physical theory allows
>objects that are not measurable and are not observable in principle.
>Let a very reliable physical theory predicts such an object. Is it
>correct to say that such object exists?
Suppose you have just fallen from a 100 storey building.
In principle, you will die in moments.
Does the Andromeda galaxy exist at the present time?
You will never observe it.
-- Toby
to...@ugcs.caltech.edu
Eugeny Kornienko
> since we supposedly know the location of all the matter exactly
> (hence a point) we cannot know the momentum of that point. It would
> thus be possible to quantum mechanically tunnel out of the black
> hole! Or what's worse: we would not know where the darn thing was
> going!
Do you mean that we cannot know which matter tunnels to which location
and which was the form of the matter? So "the form of matter in the
singularity" is absolutely indifferent to any observable phenomena.
Mere "a matter" or "mass" describe it enough!
> I would say that in fact the matter is measurable. Hawking showed
> the black holes to have entropy. We see matter "leaking out".
So the leaking matter is measurable, but its properties only depend on
properties of surrounding observable space where the matter appears.
This phenomenon doesn't depend on "form of matter" beneath event
horizon.
On Thursday, May 06, 1999, Toby Bartels <to...@ugcs.caltech.edu> wrote
> beneath the event horizon does *not* equal at the singularity!
> There's quite a bit of spacetime between the horizon and the
> singularity.
Yes. Practically the spacetime beneath event horizon is empty because
matter falls into the singularity in seconds. I'm not physicist, only
a curious man. I'm waiting until somebody reveals the quantum tornado
that raves near the singularity. Perhaps Hawking's black hole
evaporation is a tiny cue to this tornado.
> GTR does not *require* the existence of disconnected universes
It doesn't forbid them, too.
> Ockham would have us believe in the latter but not the former (at
> least not on the basis of reason alone).
I think the "reason alone" may force us to accept the existence of
disconnected universes. Ultimately physics will explain internal
causes of Big Bang - how the spacetime and matter emerge from nothing.
If the emerging is possible hence it is inevitable. (Is it clear?)
Hence any amount of such disconnected Big Bangs must emerge and exist.
>> Let a very reliable physical theory predicts such an object. Is it
>> correct to say that such object exists?
> Suppose you have just fallen from a 100 storey building...
You vulgarize the idea. :) I don't worry about my personal ability to
watch Andromeda galaxy. I only hope that these possible disconnected
spacetimes are not absolutely disconnected. If it will be discovered a
(quantum) mechanism of tunneling between them then the mechanism might
feed the dynamics of our quantum vacuum because "emerging from
nothing" is the very dynamics. It's interesting to me; do physicists
work on origin of space (vacuum) or only on explaining of observable
properties of the space? Sure it's mostly the same problem. :)
Eugeny Kornienko
Toby Bartels
>Toby Bartels <to...@ugcs.caltech.edu> wrote:
>>beneath the event horizon does *not* equal at the singularity!
>>There's quite a bit of spacetime between the horizon and the
>>singularity.
>Yes. Practically the spacetime beneath event horizon is empty because
>matter falls into the singularity in seconds.
Not necessarily. It depends how big the black hole is.
Even in a normally sized case, matter could fall in continuously,
so the space in between is refilled as fast as it empties.
>I think the "reason alone" may force us to accept the existence of
>disconnected universes. Ultimately physics will explain internal
>causes of Big Bang - how the spacetime and matter emerge from nothing.
>If the emerging is possible hence it is inevitable. (Is it clear?)
>Hence any amount of such disconnected Big Bangs must emerge and exist.
You seem quite eager to draw corollaries from a theory
that hasn't been put forth yet.
>>Suppose you have just fallen from a 100 storey building...
>You vulgarize the idea. :) I don't worry about my personal ability to
>watch Andromeda galaxy.
Then why worry about your personal ability
to watch the inside of a black hole?
I really think they're comparable.
-- Toby
to...@ugcs.caltech.edu