Why don't all neutron stars collapse into black holes?

[dect117]

If they are so insanely dense and their gravity is so mind-numbingly great, what prevents a neutron star from immediately collapsing into a black hole?

 

[phinds]

Have you looked into what it takes for a mass to form a black hole?

 

[SteamKing]

If they are so insanely dense and their gravity is so mind-numbingly great, what prevents a neutron star from immediately collapsing into a black hole?

Because neutron stars, although "insanely dense" and having "mind-numbingly great" gravity, are not dense enough, nor do they possesses sufficient gravity, to form a black hole.

 

[Hornbein]

If they are so insanely dense and their gravity is so mind-numbingly great, what prevents a neutron star from immediately collapsing into a black hole?

It's the Pauli exclusion principle, the same thing that keeps YOU from collapsing into a man-mass black hole.

 

[phinds]

It's the Pauli exclusion principle, the same thing that keeps YOU from collapsing into a man-mass black hole.

It would seem that, by that logic, black holes could never form at all. Is that what you believe?

 

[Hornbein]

It would seem that, by that logic, black holes could never form at all. Is that what you believe?

? The Pauli exclusion principle prevents neutron stars from collapsing into black holes. If you want to read more into my post than that, it is up to you.

 

[phinds]

? The Pauli exclusion principle prevents neutron stars from collapsing into black holes. If you want to read more into my post than that, it is up to you.

My point is, I'm asking why you think it doesn't prevent other things from collapsing into black holes. You do realize that a neutron star DOES collapse into a black hole if enough more mass is added?

 

[Hornbein]

My point is, I'm asking why you think it doesn't prevent other things from collapsing into black holes. You do realize that a neutron star DOES collapse into a black hole if enough more mass is added?

Yes, I know that. How kind of you be concerned about the state of my knowledge. However, that is not the question the original poster asked. I would welcome any attempt by you to answer your own rhetorical question.

 

[phinds]

Yes, I know that. How kind of you be concerned about the state of my knowledge. However, that is not the question the original poster asked. I would welcome any attempt by you to answer your own rhetorical question.

We seem to be talking past each other. I take it you agree w/ me that the Pauli Exlcusion Principle keeps a neutron star from collapsing into a black hole, right up to the point where it doesn't keep it from doing that any more.

My point being that it isn't really the Pauli exclusion principle that keeps it from collapsing into a black hole, it's the absence of enough mass. Given enough mass the exclusion principle becomes irrelevant. This is what I was trying, in post #2, to get the OP to research out for himself.

 

[Drakkith]

My point being that it isn't really the Pauli exclusion principle that keeps it from collapsing into a black hole, it's the absence of enough mass.

The PEP keeps matter from collapsing into a small enough volume to form a black hole, regardless of how massive the object is. In any case, there's really no single cause of all this, it's a combination of many different factors.

Edit: To elaborate, I mean that without the PEP objects of any nearly any mass would collapse into black holes.

 

[phinds]

The PEP keeps matter from collapsing into a small enough volume to form a black hole, regardless of how massive the object is.

How does that not imply that black holes can't form at all?

 

[Drakkith]

How does that not imply that black holes can't form at all?

Because it's only a simple description of what happens? If I told you that the EM force keeps you from collapsing into a pile of mush due to gravity, does that imply that objects can be any size and not have to worry about collapsing? Certainly not!

Edit: I just re-read my post. It does seem to imply exactly what you said. I've edited it.

 

[phinds]

Edit: I just re-read my post. It does seem to imply exactly what you said. I've edited it.

OK, THAT I agree with.

 

[Chronos]

One of the basic premises in QM is no physical object can be smaller than its Schrodinger wavelength.

 

[AgentSmith]

Does not degeneracy pressure keep a neutron star from further collapse? And a black hole's gravity overcomes the degeneracy pressure? So whether a star becomes one or the other depends on its mass.

 

[newjerseyrunner]

One of the basic premises in QM is no physical object can be smaller than its Schrodinger wavelength.

Tangent question: Does Hawking radiation at the event horizon have an infinitesimal wavelength?

 

[mfb]

Does not degeneracy pressure keep a neutron star from further collapse?

Degeneracy pressure is a result of the PEP.

And a black hole's gravity overcomes the degeneracy pressure? So whether a star becomes one or the other depends on its mass.

Right.

Tangent question: Does Hawking radiation at the event horizon have an infinitesimal wavelength?

That's related to the firewall problem.
It certainly has a large wavelength far away, where the emission process is quite well understood.

 

[Ken G]

There is a relatively straightforward answer to why some things eventually collapse into black holes, and others do not, and it basically depends on their mass, but there's a lot more to the story. First of all, we must recognize that all objects in force balance (even if only to a good approximation, because they are actually slowly evolving) obey something called the "virial theorem." This means there is a tight connection between their internal kinetic energy, and their internal potential energy. In the case of massive objects in danger of becoming black holes, the potential energy is gravitational.

As long as an object has the necessary relation between kinetic energy and potential energy, be it the Sun or a neutron star, it will be in force balance. But there is another key issue, which relates to stability, which means, if you take a little heat out of the object (which means remove some of that kinetic energy), how much does the object need to contract, and release gravitational energy, in order to recover force balance, i.e., in order to recover the necessary ratio of kinetic energy to gravitational potential energy? The answer to that is crucial, and it depends on what is the necessary ratio to have force balance, which turns out to depend on how relativistic or nonrelativistic are the particles that have the kinetic energy.

The reason that is crucial is, the necessary ratio of kinetic energy to potential energy (in the absolute value of the latter) is 1 to 2 for nonrelativistic particles, but nearly 1 to 1 for highly relativistic particles (such as you find in neutron stars that are close to becoming black holes). You can see why that difference is so crucial, if you start out with a nonrelativistic case and remove x heat so the kinetic energy becomes 1-x and the potential energy is still 2, you don't have enough kinetic energy. So the star contracts, releasing y potential energy, so it's kinetic energy becomes 1-x+y and its potential becomes 2+y (in the absolute value). The ratio needs to solve (1-x+y)/(2+y) = 1/2 to recover force balance, and that is solved by y=2x. No problem, if x is small, y can be small too, and the star need only contract a little each time it loses heat.

But what if we have the relativistic case? Then the ratio is nearly 1 to 1, so we have nearly the equation (1-x+y)/(1+y)=1, and the solution to that requires a very large y even if x is small! That's the problem that leads to black holes. A small loss of heat produces big contraction, which raises the energy scale dramatically, and new processes become possible. Some of those new processes are endothermic-- they eat up heat! So we have a thermal runaway, causing rapid collapse: a black hole.

So there's your answer-- the neutron star becomes a black hole when the neutrons go highly relativistic.

Now, before I stop there, you should notice two things I did not mention: the mass of the neutron star, and the Pauli exclusion principle. As mentioned above, those are both going to be important, in a related way. The story I told so far seems to suggest everything would eventually lose enough heat to contract enough to go relativistic, and become a black hole. But that doesn't happen, for one reason only: systems have a quantum mechanical ground state, which is a state from which they can lose no more heat. Thus, x=0, and if you are in a force balance by that point, you just stay there-- no further contraction, no black hole. You don't even need a PEP, just a quantum ground state, but the PEP controls what that ground state will actually be. So we'd still have a boundary between what does and does not collapse to a black hole even without a PEP, but the PEP tells you at what mass that distinction is set-- it is whatever mass reaches its quantum ground state just before the particles carrying the kinetic energy go too relativistic and become too unstable. For a neutron star, that is somewhere around 3 solar masses, though it is not known exactly because no one is sure about what the quantum mechanical ground state of a neutron star will actually be.

 

[Hornbein]

There is a relatively straightforward answer to why some things eventually collapse into black holes, and others do not, and it basically depends on their mass, but there's a lot more to the story. First of all, we must recognize that all objects in force balance (even if only to a good approximation, because they are actually slowly evolving) obey something called the "virial theorem." This means there is a tight connection between their internal kinetic energy, and their internal potential energy. In the case of massive objects in danger of becoming black holes, the potential energy is gravitational.

As long as an object has the necessary relation between kinetic energy and potential energy, be it the Sun or a neutron star, it will be in force balance. But there is another key issue, which relates to stability, which means, if you take a little heat out of the object (which means remove some of that kinetic energy), how much does the object need to contract, and release gravitational energy, in order to recover force balance, i.e., in order to recover the necessary ratio of kinetic energy to gravitational potential energy? The answer to that is crucial, and it depends on what is the necessary ratio to have force balance, which turns out to depend on how relativistic or nonrelativistic are the particles that have the kinetic energy.

The reason that is crucial is, the necessary ratio of kinetic energy to potential energy (in the absolute value of the latter) is 1 to 2 for nonrelativistic particles, but nearly 1 to 1 for highly relativistic particles (such as you find in neutron stars that are close to becoming black holes). You can see why that difference is so crucial, if you start out with a nonrelativistic case and remove x heat so the kinetic energy becomes 1-x and the potential energy is still 2, you don't have enough kinetic energy. So the star contracts, releasing y potential energy, so it's kinetic energy becomes 1-x+y and its potential becomes 2+y (in the absolute value). The ratio needs to solve (1-x+y)/(2+y) = 1/2 to recover force balance, and that is solved by y=2x. No problem, if x is small, y can be small too, and the star need only contract a little each time it loses heat.

But what if we have the relativistic case? Then the ratio is nearly 1 to 1, so we have nearly the equation (1-x+y)/(1+y)=1, and the solution to that requires a very large y even if x is small! That's the problem that leads to black holes. A small loss of heat produces big contraction, which raises the energy scale dramatically, and new processes become possible. Some of those new processes are endothermic-- they eat up heat! So we have a thermal runaway, causing rapid collapse: a black hole.

So there's your answer-- the neutron star becomes a black hole when the neutrons go highly relativistic.

Now, before I stop there, you should notice two things I did not mention: the mass of the neutron star, and the Pauli exclusion principle. As mentioned above, those are both going to be important, in a related way. The story I told so far seems to suggest everything would eventually lose enough heat to contract enough to go relativistic, and become a black hole. But that doesn't happen, for one reason only: systems have a quantum mechanical ground state, which is a state from which they can lose no more heat. Thus, x=0, and if you are in a force balance by that point, you just stay there-- no further contraction, no black hole. You don't even need a PEP, just a quantum ground state, but the PEP controls what that ground state will actually be. So we'd still have a boundary between what does and does not collapse to a black hole even without a PEP, but the PEP tells you at what mass that distinction is set-- it is whatever mass reaches its quantum ground state just before the particles carrying the kinetic energy go too relativistic and become too unstable. For a neutron star, that is somewhere around 3 solar masses, though it is not known exactly because no one is sure about what the quantum mechanical ground state of a neutron star will actually be.

This is really interesting. I wonder though. I have read that in a neutron star only the electrons are relativistic. The amount of such mass is fairly small.

 

[Ken G]

It depends on how close to becoming a black hole the neutron star is. When the neutron star is getting close to its mass limit, the neutrons are also going relativistic, as this is the cause of the mass limit in the first place. But this is something of a simplification, because there might also be other things in there, like free quarks in the core and who knows what. You're right that the electrons would be ultrarelativistic, and not very important.

 

[Hornbein]

It depends on how close to becoming a black hole the neutron star is. When the neutron star is getting close to its mass limit, the neutrons are also going relativistic, as this is the cause of the mass limit in the first place. But this is something of a simplification, because there might also be other things in there, like free quarks in the core and who knows what. You're right that the electrons would be ultrarelativistic, and not very important.

Aha. I have long been puzzled by this. By relativistic it is meant that the particles are moving at high speeds relative to one another. But the core of a neutron star is superfluid, so in a sense the neutrons aren't moving at all. I guess temperature is the amount of kinetic energy that something contains, but I don't know what the definition of the temperature of a hot superfluid is. I don't understand the situation enough to formulate a question, so this will have to do.

 

[Ken G]

Temperature isn't the right way to think about it, because temperature is a thermodynamic property that deals with ability to lose heat. But pressure just depends on the kinetic energy, so think kinetic energy rather than temperature. For example, if you take a simple hydrogen atom down to zero temperature, the electron in there will have about 6.8 eV of kinetic energy, which is quite a lot! In a neutron star, the particles are bound only by the overall gravity, but the pressure still comes from their kinetic energy. So the key issue about how relativistic they are is the ratio of pressure to kinetic energy density. When that ratio falls to near 1/3, which it does as the particles get more and more relativistic, watch out. You're right that "kinetic energy" isn't quite the same thing as "motion", because we can say that a ground state is a "stationary state" wherein it gets a little unclear if the particles should be regarded as "moving" or just having a complex oscillating wavefunction. But the distinction isn't really important-- there's still kinetic energy, and there's still pressure.

 

[Endan Rarity]

There are multiple steps to gravity description that seems to make this possible. They don't collapse because each are transversal to different dimensions, I think...

 

[Drakkith]

There are multiple steps to gravity description that seems to make this possible. They don't collapse because each are transversal to different dimensions, I think...

Err...what? That doesn't seem to make any sense.