Gravitational collapse

  • Thread starter Chimps
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  • #26
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Yes, I completely agree.

Therefore, as I said, in cannot be reached (or formed) in finite time.
 
  • #27
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I think here is a heart of confusion.
You think that as far from singularity we have time at 100%, and in the singularity time does not exist (0%), then close to the singularity it must gradually 'fade' from 100% to 0%

Not at all! Nobody promised you that it is continuus. Singularity itself is non-continuity
ANd finally it is not like 100%->50%->0%. It is rather like 100%->100%->N/A
I disagree. It cannot be 100%->100%->N/A since that would mean infinity can be reached which is clearly absurd.
 
  • #28
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What Dmitry means, is that you can't have regions which are semi-singular.
 
  • #29
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Noone is disputing that we can't know the nature of a singularity.

The dispute regards the approach towards such an anomaly.
 
  • #30
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Chimps, you are talking about something does not really exist: singularities.

As Wallace told you, singularities are just a flaw of GR. Exist just within that theory.
With other words, GR are trying to explain phenomenons for who doesn't have right tools.

To describe correctly singularities we need a theory undeveloped yet: quantum gravity.
 
  • #31
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I'm not talking about the singularity, as I have already said.

I'm talking about the observer heading towards the singularity.
 
  • #32
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I disagree. It cannot be 100%->100%->N/A since that would mean infinity can be reached which is clearly absurd.
Take y=1/x
say, x=0.1
Now move position of x by -0.1 (finite movement)
Do you 'reach the singularity'? :)

I dont follow your logic. Looks like it is based on too many 'common sense assumptions' which are not valid. Could you get rid of the words 'clearly', 'absurd' and try to explain your logic? You can start from giving any mathematical definition of what "reaching the infinity" means.
 
  • #33
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I'm not talking about the singularity, as I have already said.

I'm talking about the observer heading towards the singularity.
If you are not talking about the singularity itself, then GR is accurately describing what happens. The length of a worldline of freely falling observer is finite. So one cant say that "it takes infinite time to reach the singularity".
 
  • #34
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Take y=1/x
say, x=0.1
Now move position of x by -0.1 (finite movement)
Well, for a start, that move becomes meaningless in this discussion because you are not including the existence/non-existence of time.
 
  • #35
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Well, for a start, that move becomes meaningless in this discussion because you are not including the existence/non-existence of time.
Wait :)
Just 1 post ago you claimed that:

I'm not talking about the singularity, as I have already said.

I'm talking about the observer heading towards the singularity.
If you are not talking about the singularity, then you are talking about the area of spacetime correctly defined in GR. So there is no place where you can start talking about "non-existence of time"

In GR time exists everywhere except the singularity, where GR gives an answer "N/A", not "Time does not exist" as you might think.
 
  • #36
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If you are not talking about the singularity itself, then GR is accurately describing what happens. The length of a worldline of freely falling observer is finite. So one cant say that "it takes infinite time to reach the singularity".
As we established - it is beyond GR. I am not disputing that. It is time itself which is the 'on or off'. It's like constantly halving a ruler. From our perspective time is infinite so any attempts to spacially reconcile a singularity are pointless.
 
  • #37
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For me, inside a black hole, at its centre exist a very strange kind of object, extremely dense (but finite), with a finite diameter and a huge temperature (but also finite).
I don't have arguments, but I strongly believe that in Universe nothing can be reduced to a size beyond Planck length, even inside a BH.

All falling matter is broken down in quarks and leptons (possible in strings) and is added to that core. And if all matter in Universe will be added in just one black hole its core will be still bigger than Planck length. But then an other phenomena will happen: a Big Bounce.

So, a falling observer will be simply broken in basic elements and will be added to BH core in finite observer time.

Edit: But as I said, this is my idea of BH inside. Something like this avoid strange things like singularities.
 
Last edited:
  • #38
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As we established - it is beyond GR. I am not disputing that. It is time itself which is the 'on or off'. It's like constantly halving a ruler. From our perspective time is infinite so any attempts to spacially reconcile a singularity are pointless.
Even if time in GR is not defined at singularity, the time-like distance to it is well defined in GR, and it is finite.

I can give you an example. Take a line from 0 to infinity: [0,inf[
We are at x=1, so the distance to x=0 is 1-0=1.

Now we EXCLUDE point x=0. Say, for some reason our theory does not work at x=0.
So instead of [0,inf[ we have open set from both sides: ]0,inf[
Still, the distance from x=1 to x=0 is well defined and it is not infinite.

So even GR does not say anything about the singularity itself, the timelike distance to singularity is well defined in GR. There is no places where you can apply any form of Zeno paradox with "constantly halving a ruler"
 
  • #39
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For me, inside a black hole, at its centre exist a very strange kind of object, extremely dense (but finite), with a finite diameter and a huge temperature (but also finite).
I don't have arguments, but I strongly believe that in Universe nothing can be reduced to a size beyond Planck length, even inside a BH.

All falling matter is broken down in quarks and leptons (possible in strings) and is added to that core. And if all matter in Universe will be added in just one black hole its core will be still bigger than Planck length. But then an other phenomena will happen: a Big Bounce.

So, a falling observer will be simply broken in basic elements and will be added to BH core in finite observer time.

Edit: But as I said, this is my idea of BH inside. Something like this avoid strange things like singularities.
Yes. I have some arguments that it is much bigger then Plank length (but still very small). I need to make some calculations.
 
  • #40
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Even if time in GR is not defined at singularity, the time-like distance to it is well defined in GR, and it is finite.

I can give you an example. Take a line from 0 to infinity: [0,inf[
We are at x=1, so the distance to x=0 is 1-0=1.

Now we EXCLUDE point x=0. Say, for some reason our theory does not work at x=0.
So instead of [0,inf[ we have open set from both sides: ]0,inf[
Still, the distance from x=1 to x=0 is well defined and it is not infinite.

So even GR does not say anything about the singularity itself, the timelike distance to singularity is well defined in GR. There is no places where you can apply any form of Zeno paradox with "constantly halving a ruler"
The ruler analogy was poor and didn't represent my argument very well so please ignore that.

My argument does not consist of any form of Zeno paradox. Your example is not sufficient when considering spacetime. There is no point zero as such which can represent a singularity. There is only a point (if you want to call it such) in which you would be heading towards infinity.
 
  • #41
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This is exactly my example: there is no such point (x=0) so when you approach x->0 you are 'heading towards infinity'. Still distance is well defined.

You you believe other sources:
http://en.wikipedia.org/wiki/Schwarzschild_radius
and showed that the dust particles could reach the singularity in finite proper time.
 
  • #42
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I hate to get too philisophical on this mater, but it seems to me that instead of asking what you would observe after crossing the event horizon, a more appropriate question would be "could you continue to exist in a state that would even allow observation".

We make our observations in 4-dimensional spacetime. I think the problem is that at the event horizon, these 4 dimensions cease to exist in the same way as they do on our side of the horizon. Furthermore, it would seem to me that the mass of your body could not exist in the same way once crossing that horizon.

So, since all human observation is 4-dimensional, how can you measure something outside of those 4 dimensions?
 
  • #43
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Marcellus, GR is very accurate, you continue to exist and you will continue to observe.
Even more, you can actually fall into a supermassive BH without even noticing it.
 
  • #44
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This is exactly my example: there is no such point (x=0) so when you approach x->0 you are 'heading towards infinity'. Still distance is well defined.

You you believe other sources:
http://en.wikipedia.org/wiki/Schwarzschild_radius
I can't see how this is consistent with the position you took earlier. Also, why are you linking to an article about the Schwarzschild radius?

The distance is not well defined, in a spacetime scenario, the distance is impossible to define.
 
  • #45
George Jones
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The Schwarzschild radius associated with a mass [itex]m[/itex] is [itex]2Gm/c^2[/itex], so I don't know what you mean by
I can't see how this is consistent with the position you took earlier. Also, why are you linking to an article about the Schwarzschild radius?

The distance is not well defined, in a spacetime scenario, the distance is impossible to define.
Could you elaborate?
 

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