Quote: Original post by Krokhin

Quote:
As for black hole formation, it takes only elementary general relativity to show that it does not take an infinite amount of time for matter to fall to the centre. A year or two back a couple of people tried to show that matter instead gets stuck on its way to the event horizon, never passing it. That's a basic confusion about the time coordinate (see Kruskal-Szekeres coordinates versus the highly flawed Schwarzschild coordinates). How the paper ever got recognition was a great mystery to pretty much every physicist that I talked to about it.

May be,but in which time-coordinate system? As for me,I prefer my system,faraway from this outrage[smile]

Um... "see Kruskal-Szekeres coordinates versus the highly flawed Schwarzschild coordinates".

Quote: Original post by taby

Quote: Original post by Krokhin

Quote:
As for black hole formation, it takes only elementary general relativity to show that it does not take an infinite amount of time for matter to fall to the centre. A year or two back a couple of people tried to show that matter instead gets stuck on its way to the event horizon, never passing it. That's a basic confusion about the time coordinate (see Kruskal-Szekeres coordinates versus the highly flawed Schwarzschild coordinates). How the paper ever got recognition was a great mystery to pretty much every physicist that I talked to about it.

May be,but in which time-coordinate system? As for me,I prefer my system,faraway from this outrage[smile]

Um... "see Kruskal-Szekeres coordinates versus the highly flawed Schwarzschild coordinates".

Sorry,but I want to say once again that I'm not going to fall to black hole like in case of abbot's Lemetr and other coordinates.
I prefer to observe the mattery firework near the event horison at safety distance...

Quote: Original post by Krokhin

Quote: Original post by Lode
If our universe would be a giant black hole, what would such a black hole inside that black hole be?

Probably I can mistake,but a charged black hole may have two event horisons (temporal onion). After crossing of each horison time and space coordinates switch the roles,and so on.there are a lot of very interesting theories.
But in realty many things looks different-for example,the latest supernova in Magellan Cloud.Firstly, it was a blue (not red!!) supergiant star,secondly- now astronomers can see nothing on that place and discuss about: how much time the forming of event horison itself takes at all? (Here I can mistake again,cuz it's four years old data,and now may be something has apeared)

AFAIK, Oppenheimer and Snyder first looked into collapse. Check out their work if you really do want to know. Also, look into coordinate singularity versus actual singularity (see Kretschmann scalar).

Also, you may or may not want to equate the inner horizon of an electrically charged black hole with anything worth talking about. According to a lot of models, it does not contribute entropy (I agree). On the other hand, some models claim that the inner horizon subtracts from the black hole's total entropy. If that were the case, then an extremal black hole (where the inner and outer horizons are at the same radial distance) would have zero entropy. That makes little sense to me, and to a lot of physicists as well. Of course, if this were all in a multiverse, the entropy would actually be transported to the space kitten realm, so it doesn't actually vanish, thus solving the problem (sorry, I couldn't resist). ;)

Quote: Original post by Krokhin
Sorry,but I want to say once again that I'm not going to fall to black hole like in case of abbot's Lemetr and other coordinates.
I prefer to observe the mattery firework near the event horison at safety distance...

Lemaitre's metric is not the same thing as the Schwarzschild metric, regardless of whether you represent the Schwarzschild metric using Kruskal-Szekeres or Schwarzschild coordinates. What???

Quote: Original post by taby

Quote: Original post by Krokhin
Sorry,but I want to say once again that I'm not going to fall to black hole like in case of abbot's Lemetr and other coordinates.
I prefer to observe the mattery firework near the event horison at safety distance...

Lemaitre's metric is not the same thing as the Schwarzschild metric, regardless of whether you represent the Schwarzschild metric using Kruskal-Szekeres or Schwarzschild coordinates. What???

Well ,as I understand,the matter of this question is:
from outside observer's point of view time above but close to event horison runs very slow.Does it mean that everything exactly and under the event horison are in frosen state ,or not? (but agaain from outside observer's point of view).
BTW-returning to the main question of this thread-the boundary of our universe looks exactly like a black hole's event horison (exepting the reason of red shift of couse). I.e. our universe is not a black hole,but black hole around us.
(sorry for time-space delay,it's not because I'm closer to the event horison than you,just have a lot of job now)

Seeing as how it was proven mathematically (based on current theories, so not full proof of course) that the amount of time until you hit the singularity was finite... and since the closer to the singularity you got the greater the time dilation (even after the event horizon was crossed), galaxies even a tiny bit closer to the singularity would be moving at a significantly noticeable difference in speed and redshift.

So no, we're not living in a giant blackhole.

The hologram theory is an old one, and was demonstrated before hawking finally reneged on his information-loss paradox theorem (which essentially became the proof for it). It was shown that the maximum amount of data that can be stored in a volume of space is dependent upon the surface area of the space surrounding the volume (not the volume). (that is: for a 3d sphere of radius N, the maximum amount of data that can be stored is factor of the surface area of that sphere or 4πh2.

Quote: Original post by Washu
The hologram theory is an old one, and was demonstrated before hawking finally reneged on his information-loss paradox theorem (which essentially became the proof for it). It was shown that the maximum amount of data that can be stored in a volume of space is dependent upon the surface area of the space surrounding the volume (not the volume). (that is: for a 3d sphere of radius N, the maximum amount of data that can be stored is factor of the surface area of that sphere or 4πh2.

You're right Washu, I should have made that clearer. Regardless of the metric within the boundary (which in essence, could provide an arbitrarily large volume), the maximum amount of entropy within the boundary is finite. This relates to the "no universe within an atom" topic discussed earlier in this thread. AFAIK, 't Hooft stated it as "no universe in a test tube".

So in effect, even though you could fit a universe worth of space within an atom, you cannot fit a universe worth of information within an atom.

Fun fact: the A = 4\pi r^2 relation holds only for a non-rotating black hole. For a rotating black hole the horizon's surface area is not quite the same as the plain old Euclidean 2-sphere -- the metric is based not only on the radial coordinate, but on angle as well. I believe that the relation is A = 4\pi (r^2 + a^2), where a = J/(Mc), and J is angular momentum. Entropy is still proportional to area in the same way, of course.

[Edited by - taby on February 16, 2010 3:29:41 PM]

Quote: Original post by Krokhin

Quote: Original post by taby

Quote: Original post by Krokhin
Sorry,but I want to say once again that I'm not going to fall to black hole like in case of abbot's Lemetr and other coordinates.
I prefer to observe the mattery firework near the event horison at safety distance...

Lemaitre's metric is not the same thing as the Schwarzschild metric, regardless of whether you represent the Schwarzschild metric using Kruskal-Szekeres or Schwarzschild coordinates. What???

Well ,as I understand,the matter of this question is:
from outside observer's point of view time above but close to event horison runs very slow.Does it mean that everything exactly and under the event horison are in frosen state ,or not? (but agaain from outside observer's point of view).
BTW-returning to the main question of this thread-the boundary of our universe looks exactly like a black hole's event horison (exepting the reason of red shift of couse). I.e. our universe is not a black hole,but black hole around us.
(sorry for time-space delay,it's not because I'm closer to the event horison than you,just have a lot of job now)

I'm reaching the limit of where I feel comfortable with "teaching" about these things, so I'll make it quick. Like I say, I'm not a physicist, and I would feel bad about steering someone in the wrong direction.

1) No, gravitational time dilation does not cause a massive body to stop moving through space. It causes a massive body to stop moving through time. Like I say, please read up about using Kruskal coordinates. There's a bajillion google hits on the subject.

2) No, a 3D black hole's 2D event horizon does not look exactly like the boundary of the 3D universe. This is primarily because the 3D universe has no boundary to begin with! This is discussed in Einstein's book Relativity: The Special and the General Theory. I suggest that you read this book (it's free on Project Gutenberg) instead of replying, since I've already mentioned that the universe is "finite yet unbounded" once in this thread. Clearly you don't believe me (you shouldn't, I'm not a physicist). :)

[Edited by - taby on February 16, 2010 4:32:07 PM]

Krokhin, here's a much better (not hand-wavy) explanation about infall:

http://cosmology.berkeley.edu/Education/BHfaq.html#q4

I also missed the fact that your initial view was "the black hole is frozen", but in your most recent reply the view was "the black hole appears frozen". Of course, this paradigm shift is exactly what is needed to answer to your own question.

For what it's worth, I believe that my last reply is somewhat incorrect. From what I've reviewed today, it is apparently OK to assume that the body does effectively get "stuck" in space -- it's just that space itself moves toward the centre, and the body goes along for the ride. See http://casa.colorado.edu/~ajsh/schwp.html. Either way though, the infall time is finite, and so your initial view was justly objected to.

Perhaps you and hodgman can work together as a team to write up a nice little email to a physicist asking about this. I surely would love a definitive answer. Don't forget to frame the question in the context of Kruskal coordinates.

[Edited by - taby on February 16, 2010 8:51:48 PM]

Taking the holographic principle to extremes...

If one takes the radius of a hydrogen atom to be 53pm, then according to the principle we have it such that the maximum amount of data (in a non-rotating system) that can be stored is proportional to the surface area of the bounding sphere of that atom (actually, it's 1/4 of the surface area in Planck units) which is: 4π532 pm2, taking out our 1/4 we find that our result is: π53^2 pm2 or about 8825 pm2. Given the conversion ratio: 1 / 2.612x10-46 pm2 for pm^2 to Planck area's, we can simply multiply by that conversion ratio to get the maximum number of bits sortable in the volume of a hydrogen atom: 3.379x1049. Of course, properly retrieving those bits is almost impossible, as a black hole of that size would decay extremely rapidly and at rather extreme temperatures.

All math shown above is subject to being wrong in your particular universe.