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Author Topic: From neutron star to Black Hole...........?  (Read 24931 times)

Ethos

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From neutron star to Black Hole...........?
« on: 09/04/2009 05:08:44 »
Maybe one of you fellows can answer a question for me?

Let's imagine that we have the means to experiment with a neutron star. Parking ourselves close enough for our experiment, we aim a neutron gun at the star and begin to inject neutrons into it at a controled rate. This experiment is being preformed with the goal of finding out exactly how much mass needs to accumulate within the body before it becomes a Black Hole. Keeping in mind that care is taken not to add neutrons so fast that it's equilibrium is upset resulting in an explosive event.

My question is: What is the least amount of mass we must accumulate within this neutron star to transform it into a Black Hole?

I have a book by John Archibald Wheeler that draws conclusions about Black Hole formation but he does not investigate this particular method for Black Hole creation. I believe the method I've purposed would create a Black Hole with the least amount of perturbation, and the resulting figures for the mass and compaction could be viewed as a universal constant of sorts. This threshold, between our universe and what lies beyond within the Black Hole, should be an important commological plateau that must surely hold much significance.....................Ethos


 

Offline Raghavendra

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From neutron star to Black Hole...........?
« Reply #1 on: 09/04/2009 07:49:20 »
I will answer this question?
 

Offline Soul Surfer

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From neutron star to Black Hole...........?
« Reply #2 on: 10/04/2009 19:37:07 »
It is a good deal less than the mass of a typical neutron star but probably more than ten percent of the mass of the neutron star exactly how much depends on the mass of the neutron star which is not totally fixed. The collapse process may go through a slightly more dense stable state called a quark star before becoming a black hole where the neutrond collpse and individual quarks have asymptototic freedom.  Neutron stars are quite close to being black holes and cause very significant distortions to space time
 

Offline LeeE

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From neutron star to Black Hole...........?
« Reply #3 on: 10/04/2009 21:33:11 »
I don't think that simply adding mass to a neutron star would work.

In adding mass, you're just adding to the quantity of matter but for a black hole to form you need to increase the density.  Unless there is an upper limit to the size that neutrons stars can achieve (not to be confused with the maximum size of a neutron star that can be created) you're just going to create a bigger neutron star.

To turn a neutron star in to a black hole you'd need to compress it, not just make it bigger.

With a small enough neutron star though, you might be able to compress it explosively, in a similar sort of manner to the way that fission bomb sub-critical mass cores are compressed to a critical mass, to get it dense enough.
 

Ethos

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From neutron star to Black Hole...........?
« Reply #4 on: 11/04/2009 01:13:23 »
I don't think that simply adding mass to a neutron star would work.

To turn a neutron star in to a black hole you'd need to compress it, not just make it bigger.

Wouldn't compression come as a result of the added gravitational attraction? That is, if I understand correctly, the driving force behind all Black Hole formation anyway..........Ethos
 

Offline Vern

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From neutron star to Black Hole...........?
« Reply #5 on: 11/04/2009 23:43:55 »
Quote from: LeeE
I don't think that simply adding mass to a neutron star would work.
This should be solvable. We know the density of neutron stars. There should be a way to compute a size where that density would not allow light to escape. That would be a black hole, in effect, however there need not be a singularity at its centre.
 

Ethos

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From neutron star to Black Hole...........?
« Reply #6 on: 12/04/2009 02:29:46 »
Quote from: LeeE
I don't think that simply adding mass to a neutron star would work.
This should be solvable. We know the density of neutron stars. There should be a way to compute a size where that density would not allow light to escape. That would be a black hole, in effect, however there need not be a singularity at its centre.

Astute observation Vern, I hadn't considered that particular twist.

When this threshold of mass density is achieved, I believe we could establish a new natural constant of nature. In some respects, this new ground state of Black Hole structure might represent an entity as basic as the electorn itself. One might argue that this structure is unique enough to refer to it as a single particle. I realize that statment takes a leap of imagination but, it may be interesting to examine this possibility. If we can think in terms of the electron being the smallest unit of mass in the natural world, this new structure might be viewed as the largest. Everything which lies between these two states is everything we understand about matter. Might be very interesting to know the results for this following equation:

Let me equal the mass of the electron
Let Mo equal the mass of our hypothetical neutron star

I would like to know the answer to (Mo/me)

......................Ethos
 

Offline Mr. Scientist

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From neutron star to Black Hole...........?
« Reply #7 on: 12/04/2009 02:39:50 »
Maybe one of you fellows can answer a question for me?

Let's imagine that we have the means to experiment with a neutron star. Parking ourselves close enough for our experiment, we aim a neutron gun at the star and begin to inject neutrons into it at a controled rate. This experiment is being preformed with the goal of finding out exactly how much mass needs to accumulate within the body before it becomes a Black Hole. Keeping in mind that care is taken not to add neutrons so fast that it's equilibrium is upset resulting in an explosive event.

My question is: What is the least amount of mass we must accumulate within this neutron star to transform it into a Black Hole?

I have a book by John Archibald Wheeler that draws conclusions about Black Hole formation but he does not investigate this particular method for Black Hole creation. I believe the method I've purposed would create a Black Hole with the least amount of perturbation, and the resulting figures for the mass and compaction could be viewed as a universal constant of sorts. This threshold, between our universe and what lies beyond within the Black Hole, should be an important commological plateau that must surely hold much significance.....................Ethos

Even if you fired the particles at the neutron star, mankind will probably have died out before seeing anything spectacular. Needless to say also, a rule called the uncertainty between time and energy given as \Delta E \Delta t \approx \hbar. This meddles up any exact calculation on the mass as well, simply because according to this equation, it would be, indeterminable.
 

Offline Vern

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From neutron star to Black Hole...........?
« Reply #8 on: 12/04/2009 16:35:23 »
Quote from: Ethos
Let me equal the mass of the electron
Let Mo equal the mass of our hypothetical neutron star

I would like to know the answer to (Mo/me)

......................Ethos
Yes; that would be interesting. There should be such a size for a neutron star. It might be possible even for ordinary matter, but since we don't observe any such monsters, there is probably a limiting factor on the size of objects. My guess is the limiting factor would be gravity.
 

Offline JP

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From neutron star to Black Hole...........?
« Reply #9 on: 13/04/2009 02:38:19 »
Quote from: LeeE
I don't think that simply adding mass to a neutron star would work.
This should be solvable. We know the density of neutron stars. There should be a way to compute a size where that density would not allow light to escape. That would be a black hole, in effect, however there need not be a singularity at its centre.


We can assume a basic model of a non-rotating neutron star, made of matter of density ρ.  A non-rotating object will collapse into a black hole if it falls within its own Schwarzschild radius.  The equation for this radius is:

rs=K m,

where K=2Gc-2 is a constant that includes on the speed of light and the gravitational constant and m is the mass of the object.  Now, there's a simple relation between mass and density, (and we'll assume a spherical object):
m=4/3π r3ρ .

Plugging this into the mass above...

rs=[3/(4Kρπ)]1/2

I plugged in some numbers from wikipedia for the density of a neutron star 5x1017kg/m3, and got

rs≈18 km.


Edit: Fixed the error LeeE pointed out.
« Last Edit: 15/04/2009 01:11:11 by jpetruccelli »
 

Offline JP

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From neutron star to Black Hole...........?
« Reply #10 on: 13/04/2009 02:42:32 »
And I think this corresponds to somewhere in the ballpark of 6 solar masses for a neutron star of that radius.  All this is a very rough approximation since real neutron stars are likely rotating and not of uniform density.  In fact, we don't even have a good handle on the physics going on inside of neutron stars.
 

Ethos

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From neutron star to Black Hole...........?
« Reply #11 on: 13/04/2009 04:00:24 »
  In fact, we don't even have a good handle on the physics going on inside of neutron stars.
Good points jpet...., I suppose one needs to look beyond the neutron star to the possible formation of a quark and gluon star. I think my imagination has reached well beyond our present ability to correctly analyze such objects. Sadly, it may be many years before we can answer the question I presented with the opening of this thread. Nevertheless, I believe the answer to this question should shed much light on the nature of matter................Ethos
 

Offline Vern

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From neutron star to Black Hole...........?
« Reply #12 on: 14/04/2009 03:39:32 »
Quote from: jpetruccelli
We can assume a basic model of a non-rotating neutron star, made of matter of density ρ.  A non-rotating object will collapse into a black hole if it falls within its own Schwarzschild radius.  The equation for this radius is:

rs=K m,
Are we sure about the collapse here? I don't remember a requirement for this. Maybe I missed it, but I didn't realize there was something magical about the Schwarzschild radius that would initiate a collapse into a singularity.
 

Offline JP

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From neutron star to Black Hole...........?
« Reply #13 on: 14/04/2009 06:19:25 »
Yes.  The Schwarzschild solution is valid outside of the nonrotating spherically symmetric object.  If the object falls within its Schwarzschild radius, then there is a region of space (within the radius, but outside the object) where the only valid space-time paths are pointed towards the center of the object.  This should ensure the collapse of the object.
 

Offline LeeE

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From neutron star to Black Hole...........?
« Reply #14 on: 15/04/2009 00:51:43 »
Quote from: LeeE
I don't think that simply adding mass to a neutron star would work.
This should be solvable. We know the density of neutron stars. There should be a way to compute a size where that density would not allow light to escape. That would be a black hole, in effect, however there need not be a singularity at its centre.


We can assume a basic model of a non-rotating neutron star, made of matter of density ρ.  A non-rotating object will collapse into a black hole if it falls within its own Schwarzschild radius.  The equation for this radius is:

rs=K m,

where K=2Gc-2 is a constant that includes on the speed of light and the gravitational constant and m is the mass of the object.  Now, there's a simple relation between mass and density, (and we'll assume a spherical object):
m=4/3π r3.

Plugging this into the mass above...

rs=[3/(4Kρπ)]1/2

I plugged in some numbers from wikipedia for the density of a neutron star 5x1017kg/m3, and got

rs≈18 km.


Umm...

Quote
m=4/3π r3

shouldn't that be V=4/3π r3?

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.
 

Ethos

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From neutron star to Black Hole...........?
« Reply #15 on: 15/04/2009 01:05:09 »

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.
I believe he posted these figures: (5X10^17kg/m^3) If you'll notice, this is where the mass, in kg's, is specified..............Ethos
 

Ethos

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From neutron star to Black Hole...........?
« Reply #16 on: 15/04/2009 01:09:32 »
From what I've learned, the equation; r = 2G X m/c^2 represents the calculation for the radius of the schartzchild metric. In truth, you can plug in any figure for the mass in this equation and determine the radius at which it will become a Black Hole.

...................Ethos
 

Offline JP

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From neutron star to Black Hole...........?
« Reply #17 on: 15/04/2009 01:10:21 »
Quote
m=4/3π r3

shouldn't that be V=4/3π r3?

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.

Oops.  I thought I clicked the button to insert a "rho."  That should read

m=4/3πr3ρ (=Volume x Density)

The rest should make sense now, since I used density instead of mass in the calculations.
« Last Edit: 15/04/2009 01:12:08 by jpetruccelli »
 

Offline LeeE

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From neutron star to Black Hole...........?
« Reply #18 on: 15/04/2009 20:14:36 »
Quote
m=4/3π r3

shouldn't that be V=4/3π r3?

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.

Oops.  I thought I clicked the button to insert a "rho."  That should read

m=4/3πr3ρ (=Volume x Density)

The rest should make sense now, since I used density instead of mass in the calculations.

If you're going to use density, you'll still have to specify either the mass or the volume, so in m=4/3πr3ρ don't you still need to specify a value for r?
 

Offline LeeE

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From neutron star to Black Hole...........?
« Reply #19 on: 15/04/2009 20:17:23 »

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.
I believe he posted these figures: (5X10^17kg/m^3) If you'll notice, this is where the mass, in kg's, is specified..............Ethos

Ethos, that's not specifying a number of kg - all it's saying is that a certain number of kg relates to a corresponding number of cubic metres for a given density.
 

Offline JP

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From neutron star to Black Hole...........?
« Reply #20 on: 16/04/2009 06:26:49 »
Quote
m=4/3π r3

shouldn't that be V=4/3π r3?

I can't see how you've arrived at rs≈18 km without specifying the mass anywhere.

Oops.  I thought I clicked the button to insert a "rho."  That should read

m=4/3πr3ρ (=Volume x Density)

The rest should make sense now, since I used density instead of mass in the calculations.

If you're going to use density, you'll still have to specify either the mass or the volume, so in m=4/3πr3ρ don't you still need to specify a value for r?

Ah... if it wasn't clear above, an object becomes a black hole when all its mass lies within the Schwarzschild radius.  I therefore set its radius (in the volume equation) equal to the Schwarzschild radius, which eliminates all my variables except for Schwarzschild radius and density.
 

Offline LeeE

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From neutron star to Black Hole...........?
« Reply #21 on: 16/04/2009 16:09:21 »
Ah yes, right - I was being a bit dim there.

It seems that the size limits for neutron star creation are quite limited - between about 1.35 and 2.1 solar masses, and they all seem to have a radius of about 12km (it would seem that the difference in their creation mass is only reflected in their density - I don't know the reason for this)

So for a neutron star to reach a radius of 18km, whilst remaining at the same average density of 4.96e+17, it would have to increase it's mass and volume by about 3.38 times.

In practice though, I suspect it's density would increase a little as mass was added, so it would collapse a little sooner, but the nova that formed the neutron star would have left relatively little matter in the region around the neutron star that could fall in to it, so it could probably only happen to a very old neutron star, or one that was propelled away from it's original location so that it could eventually acquire the extra mass from somewhere else.
 

Offline yor_on

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From neutron star to Black Hole...........?
« Reply #22 on: 17/04/2009 11:18:35 »
As far as I understand it, even if we had Neutron stars with a event horizon they still wouldn't be the same as a black hole. " One feature of black holes that should not appear around a neutron star is a last stable orbit. Around a black hole, one finds a minimum radius for the orbit of an object; inside this radius, an object must fall onto the event horizon of the black hole. This effect could only appear around a neutron star if the surface of the neutron star were inside this radius.

This would require a stellar radius that is only 50% larger than the event horizon radius, which is a result not produced by most neutron star theories. If such an object existed, however, it should be easily demonstrated, because the gravitational redshift from a neutron star with a surface at the last stable redshift is a massive 42%.

The gravitation redshift is a direct measure of the ratio of the star's mass to its radius. For this reason, the measurement of redshift is an important measure of the structure of the star, and ultimately of the behavior of the material within the neutron star."

Another reason to why I don't think Neutron stars can have a Event Horizon is that a Neutron Star then will be a 'known entiety' made out of fermions (neutrons and Protons) having a 'rigid' construction inside that star without anywhere for a neutron to decay into a "a proton and an electron, releasing a neutrino and a small amount of energy in the process. This cannot happen to a neutron in a cold neutron star because the proton would have nowhere to go; the proton must go into an energy state that at most contains only one proton, but no such state is available.

Conversely, the inverse process, the absorption of an electron by a proton to create a neutron, cannot occur because all of the available neutron energy states are filled. This is why the number of protons and neutrons in a cold neutron star are nearly identical."
http://www.astrophysicsspectator.com/topics/degeneracy/NeutronStarSize.html

Also "the neutron and proton are nearly equal in size. This is because, at the tiny distances in the nucleus, the strong nuclear force is much stronger than any of the others. Under just the strong force, protons and neutrons are effectively the same particle; this is an example of something called "isospin symmetry." And the size of them is calculated to be about a Femtometer (1 fm = 10^{-15} m = 0.000000000000001 m).

So if the definition for a black hole is a place where nothing (information) can be reflected once passed the Event Horizon, remembering that a neutron star is defined by the Pauli exclusion principle stating that there can't be two any fermions occupying the same quantum state simultaneously, then one of those definitions should be wrong? http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Astrophysics_and_the_Pauli_principle

---
That is as we suddenly would have 'information' on a Black hole as we would know the structure inside that Event Horizon. Also, how can it be able to have both a event horizon that LeeE defines as where 'time' stops, as well as then being equivalent to 'c', and still with 'ordinary fermions' being the cause of it?

But you will still be able to differ between a Neutron star and a Black Hole. "If such an object existed, however, it should be easily demonstrated, because the gravitational redshift from a neutron star with a surface at the last stable redshift is a massive 42%."

Also, if there isn't any such phenomena as Neutron stars with a event horizon then their particles (Neutrons and Protons) size together with the Pauli Exclusion Principle should help define a possible 'limit'  from where fermions might break down into 'real' Black Holes as they pass this limiting size?

 
« Last Edit: 17/04/2009 11:46:06 by yor_on »
 

Offline Vern

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From neutron star to Black Hole...........?
« Reply #23 on: 17/04/2009 17:11:15 »
If I am understanding all this correctly, it seems that to become a black hole, a neutron star must annihilate all of its matter into a quark-gluon soup, which then can collapse into a black hole. Such an event should not go unnoticed because it would produce Quasar-like energy levels.

Surely, neutron stars continuously gain mass from space debris and by cannibalizing near-by neighbours. Some should have become black holes if they existed since the universe was young.   
 

Offline yor_on

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From neutron star to Black Hole...........?
« Reply #24 on: 17/04/2009 21:20:14 »
I don't know Vern:) Nothing new with that, is there ::))
I'm not even sure in believing that a Neutron star gives us a 'limit' for where a Black hole may appear? To me it seems like a Black hole will be working from a state where fermions 'disappear' into something alike 'bosons'  for it to make sense?? And then those 'Bosons' will be 'compressed' or 'superimposed' if you like into a 'dimensionless' point inside that Black hole. And looking at it that way a Black hole seems more like a 'hole' in spacetime than anything else to me?

--
Looking on it like that it makes sense in believing that Black holes is formed at the beginning of spacetime, as we can't really have 'super vacuum cleaners' eating up all 'matter/mass'. that as if matter never reaches that 'dimensionless' point 'spacetime' will have a certain density?? Otherwise it seems to me like the universe would loose matter and? What about the law of conservation if so??
« Last Edit: 17/04/2009 21:26:14 by yor_on »
 

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From neutron star to Black Hole...........?
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