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Author Topic: Limits on gravitational collapse?  (Read 3945 times)

Offline Vern

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Limits on gravitational collapse?
« on: 12/02/2009 22:38:25 »
Does this mean we must now rethink the singularity that is assumed to be at the centre of Black Holes?

Quote from: Physical Review
    It is shown, in a simple analytic example, that an infinitesimal amount of rotation can halt the general relativistic gravitational collapse of a pressure-free cylindrical body. The example is a thin cylindrical shell (a shell with translational symmetry and rotation symmetry), made of counterrotating dust particles. Half of the particles rotate about the symmetry axis in one direction with (conserved) angular momentum per unit rest mass α, and the other half rotate in the opposite direction with the same α. It is shown, using C-energy arguments, that the shell can never collapse to a circumference smaller than C=8παΛ, where Λ is the shell's nonconserved mass per unit proper length. Equivalently, if R≡||∂/∂φ∥∂/∂z|| is the product of the lengths of the rotational and translational Killing vectors at the shell's location and λ is the shell's conserved rest mass per unit Killing length z, then the shell can never collapse smaller than R=4αλ. It is also shown that after its centrifugally induced bounce, the shell will oscillate radially and will radiate gravitational waves as it oscillates, the waves will carry away C energy, and this loss of C energy will force the shell to settle down to a static, equilibrium radius.



 

Offline Soul Surfer

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Limits on gravitational collapse?
« Reply #1 on: 12/02/2009 23:11:59 »
There never was a chance of a real point singularity because all black holes must have some angular momenum.  Look up Kerr Black hole.  What happens is not yet well understood but it is certain that infinitessimal points and infinitely thin lines do not form a part of it.

It annoys me a great deal when scientific writers rave on about singularities.  No one with any real knowledge of the subject as considered this to be likely for many years.

« Last Edit: 12/02/2009 23:19:10 by Soul Surfer »
 

Offline Vern

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Limits on gravitational collapse?
« Reply #2 on: 12/02/2009 23:47:44 »
Angular momentum seems to be absent from most black-hole studies I've seen; and you're right; it has got to be there. My thoughts were that at some point, the angular momentum and outward force should stop the collapse. The paper seemed to suggest that it might do so.

I don't know if the study could apply to black holes. I was fishing for thinking on this. :)
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #3 on: 13/02/2009 00:56:53 »
You must be very careful not to make assumptions about what goes on beyond the Schwarzchild radius of a Black Hole because at that point the rate of time has reduced to zero; what sort of meaningful physics can you do in a region that has no time dimension?  If you then consider the relationship between space and time you'll then realise that you can't speak with any authority about the size of anything beyond the Schwarzchild radius either, regardless of whether the Black Hole appears to be rotating or not.

Just about all you can be sure about is that whatever is beyond the Event Horizon of a Black Hole is not in the form of a simple mass, of a particular size, as we currently understand those concepts.
 

Offline Vern

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Limits on gravitational collapse?
« Reply #4 on: 13/02/2009 14:15:58 »
You must be very careful not to make assumptions about what goes on beyond the Schwarzchild radius of a Black Hole because at that point the rate of time has reduced to zero; what sort of meaningful physics can you do in a region that has no time dimension?  If you then consider the relationship between space and time you'll then realise that you can't speak with any authority about the size of anything beyond the Schwarzchild radius either, regardless of whether the Black Hole appears to be rotating or not.

Just about all you can be sure about is that whatever is beyond the Event Horizon of a Black Hole is not in the form of a simple mass, of a particular size, as we currently understand those concepts.
I'm beginning to suspect more and more that GR is incomplete, and some bright young student will eventually show that the singularity it predicts is only approachable and never reachable. I notice that Einstein hated singularities; too bad he didn't figure out how to remove them from his theories.
 

Offline lightarrow

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Limits on gravitational collapse?
« Reply #5 on: 13/02/2009 18:24:02 »
According to this article, there could be more naked singularities than we previously thought:
http://www.sciam.com/article.cfm?id=naked-singularities
« Last Edit: 13/02/2009 18:52:27 by lightarrow »
 

Offline Vern

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Limits on gravitational collapse?
« Reply #6 on: 13/02/2009 19:28:57 »
According to this article, there could be more naked singularities than we previously thought:
http://www.sciam.com/article.cfm?id=naked-singularities
That is a very interesting paper; I like the idea of naked singularities much better than the infinities associated with the black hole.
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #7 on: 13/02/2009 21:00:47 »
Having had a quick look at that article, I can't say I'm impressed by it.  For example, referring to whether an Event Horizon forms, or does not form, just seems to show a serious lack of understanding about the subject.

The Event Horizon is not an artifact that is created, or not created.  It simply marks the distance (the Schwarzchild radius) at which certain things reach certain values if an object is compressed to within that distance.  If an object is compressed to within it's Schwarzchild radius then the Event Horizon marks the boundary between where those values are below a finite and determinable point i.e. the rate of time and the escape velocity for the object, and where those values are above those points.

The implication therefore, behind naked singularities, is that those values are not reached at the Schwarzchild radius, and the only way that can happen is if gravity acts with a different value for the matter that forms naked singularities than it does for matter that results in non-naked singularities, without offering any reason for it to be so, or a mechanism for it to occur.
 

Offline Vern

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Limits on gravitational collapse?
« Reply #8 on: 13/02/2009 21:30:26 »
I'll have to read the paper again but I seemed to get from it that the Naked Singularity was not a singularity at all. Some mechanism as in the OP prevented the collapse from reaching the singularity. You're right, it didn't describe the mechanism, but the maths had to be there if it was a computer program that crunched the numbers.
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #9 on: 13/02/2009 21:45:47 »
Ultimately, it comes down to density; mass and volume.

The reason for the idea of singularities at the centers of Black Holes comes from the fact that in the GR scheme we aren't aware of any factors that could stop the collapse once it had reached the point where the body has collapsed inside it's Schwarzchild radius, so there's not really a mechanism to say why a singularity should form but rather that there is no mechanism that can prevent it from forming.  This is really where the QM comes in though, because it can provide a reason (intrinsic uncertainty/probability) to prevent collapse to a zero-sized point.

That is to say, if there will always be a degree of uncertainty or probability about the size of something then it cannot be resolved to precisely zero.  Hence, the QM singularity will have non-zero size whereas the Relativistic singularity will have zero size.
 

Offline Vern

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Limits on gravitational collapse?
« Reply #10 on: 13/02/2009 22:05:48 »
I was hoping for something like angular momentum to save the day and allow computation of super dense but less than infinitely dense mass. But, I guess we're not there yet.
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #11 on: 14/02/2009 21:16:05 »
I'm going to have to work out a few angular momentum solutions for quantum sized masses sometime;  just running it through my head seems to suggest a disparity between the rate of rotation for the BH as seen at the Event Horizon i.e. as a 'whole', and the hypothetical quantum sized singularity at it's center.  Hmm...   Not tonight though.
 

Offline Vern

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Limits on gravitational collapse?
« Reply #12 on: 14/02/2009 21:40:59 »
It seems to me there would be some powerful dynamics in an accretion disk as it evolved into a black hole. If galaxies give birth to black holes, they must be accretion disks first before they become black holes.

So there should be some powerful angular momentum limited only by the speed of light IMHO.
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #13 on: 14/02/2009 22:54:13 »
Accretion disks form about large bodies but do not 'evolve' in to a Black Hole; you're likely to find one around a Black Hole though.

Accretion disks consist of matter that has been drawn towards the body because of gravitational attraction and they take the form of a disk either because the matter is being drawn off from a nearby neighbour, in which case the disk will be in the same plane as the orbiting neighbour, or for the same reason that planetary nebulae end up as disks; although the matter may be falling in from any direction collisions between the particles in the halo will eventually average out the differences, leaving a disk.  I think frame-dragging may have an influence on the orientation of the disk too, but I'm not sure about that.

The key thing is though, that accretion disks form around massive bodies; the bodies must be there first, rather than the other way around.
 

Offline Vern

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Limits on gravitational collapse?
« Reply #14 on: 14/02/2009 23:06:24 »
I'm thinking about the first black hole; how did it become a black hole? It must have grown up from space debris that had relative motion between particles. This would have led to a spinning accretion disk, it seems to me. I would like to write a computer simulation of this birth of a black hole if I could get my hands on the equations of motion that would be in the simulation.

I think the program would just look at each individual particle successively and compute its future position based upon the position of all the other particles and their motion. It would be too cumbersome if each individual particle had to be computed but there might be some generalities that would allow particles to be taken as a group.   

Just from visualizing this without doing the maths, it seems to me that the growing disk would spin faster gaining relativistic mass as well as mass from the matter in the accretion disk. Just from the feel of it, and from the article in the OP, it seems it would be difficult to get the black hole to form.
« Last Edit: 14/02/2009 23:12:59 by Vern »
 

Offline LeeE

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Limits on gravitational collapse?
« Reply #15 on: 14/02/2009 23:55:30 »
Oops - I said planetary nebulae when I meant proto-planetary disk.

Have a look at:

http://en.wikipedia.org/wiki/Protoplanetary_disk
 

Offline Vern

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Limits on gravitational collapse?
« Reply #16 on: 15/02/2009 00:11:14 »
Very interesting; thanks for the link. After further investigation I find that black hole formation is suspected to come from the collapse of a super massive star. One such event was last year. This link is to an article claiming to show a video of the birth of a black hole.

Quote from: the link
ScienceDaily (Mar. 27, 2008) The date of March 19, 2008 marked the brightest ever cosmic explosion observed from the Earth. The outburst known as GRB 080319B was probably the death of a massive star leading to the creation of a black hole. For the first time the birth of a black hole has been filmed. Cameras of the "Pi of the Sky" project recorded this remarkable event with a 4-minute sequence of 10-second-long images. In almost 20 seconds the object became so bright that it could be visible with the naked eye. Then it began fading and in 4 minutes it became 100 times fainter. At that time the observation was taken over by larger telescopes.
 

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Limits on gravitational collapse?
« Reply #16 on: 15/02/2009 00:11:14 »

 

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