What's the fate of neutrons in black hole formation?

[Aliasa]

I understand how the neutron stars are formed, and why the electron degeneracy pressure collapses as electrons are absorbed by protons, by photo disintegration. However, I'm struggling to grasp what happens when the gravity is large enough to overcome neutron degeneracy pressure.

Apparently a singularity forms, but do we know the structure of matter inside a black hole? Also, if they are still in the form of fermions, how are the quantum states increased such that Pauli's exclusion principle isn't violated?

 

[mfb]

but do we know the structure of matter inside a black hole?

No. General relativity alone predicts a singularity, and it is unclear how quantum mechanics works in fields as strong as those in a black hole. The black hole will form, however - for the collapsing neutron star, the necessary pressure for an equilibrium rises faster than the degeneracy pressure created by the fermions, and becomes ill-defined at the point where a black hole forms.

 

[MacRudi]

Very good question.
first answer: we don't know
second answer: Singularity is only a mathematic conclusion out of infinite terms in the Kerr-Newmann Matrix. But we don't think, that Singularity exists in reality.
third answer: Out of String theory we think, that this kind of "supergravity" is a monopole and build a Einstein Rosen bridge. Then it would be Wormhole but for us it looks like a black hole. If we predict the cosmic censor (Hawking) that no naked singularity exists, then we cannot see it and will never see it because we have a horizont defined by Schwarzschild Radius. Mazur proved it mathematically in 1982. But if we predict naked singularities then we can fly through it and can see it. But then followed the next question if the ship would be destroyed which is flying through it. If we try to solve the problem with quantummechanics, then we have to say: Yes the ship will be destroyed. If we try to solve the problem with Stringtheory, then we get no definite answer. It could be that the string build a tube big enough to let a spaceship go through.
So the last answer is: We don't know anything ;-)

 

[PeterDonis]

Out of String theory we think, that this kind of "supergravity" is a monopole and build a Einstein Rosen bridge.

Reference, please? I don't thing "string theory" in general tells us anything this definite at this stage of our knowledge. Some particular string theory hypothesis might say something like this, but that isn't the same thing.

 

[PeterDonis]

or the collapsing neutron star, the necessary pressure for an equilibrium rises faster than the degeneracy pressure created by the fermions, and becomes ill-defined at the point where a black hole forms.

Actually, the pressure required for equilibrium diverges before the black hole forms; it diverges at 9/8 of the Schwarzschild radius.

 

[PeterDonis]

do we know the structure of matter inside a black hole?

According to classical GR, the inside of a black hole is vacuum (except just after the horizon forms, when the matter that collapsed to form the hole is still collapsing further and hasn't yet formed a singularity). So there is no "structure of matter" inside it. A black hole is not an ordinary object.

It is possible that quantum corrections change this picture, so that no singularity ever forms and the matter that collapsed inside the hole eventually "bounces" back out again. (In this case the horizon would not really be an event horizon and the black hole would not really be a black hole; it would only be an apparent horizon and an apparent black hole.) But we don't know enough about quantum gravity at this point to know whether this will happen.

 

[MacRudi]

Reference, please? I don't thing "string theory" in general tells us anything this definite at this stage of our knowledge. Some particular string theory hypothesis might say something like this, but that isn't the same thing.

you are right. This is a prediction of the superstringtheory. This is not in origin M Theory. But I'm not sure if this is working with branes also. I have to look at by myself

 

[Aliasa]

Thanks a ton for all the answers.

 

[Bernie G]

"However, I'm struggling to grasp what happens when the gravity is large enough to overcome neutron degeneracy pressure."

I think collider experiments show that when a nucleus collapses it turns into ultra relativistic quark type matter and a lot of energy. The gravitational core pressure of a 2 SM neutron star is about 1.7x10^34 kg/m^3. Its interesting that if this core was ultra relativistic and generated a pressure of (rho)(c^2)/3, the pressure would be about twice as large as 1.7x10^34 kg/m^3.

 

[Bernie G]

I'd like to retract "if the 2 SM neutron star core was ultra relativistic and generated a pressure of (rho)(c^2)/3, the pressure would be about twice as large as 1.7x10^34 kg/m^3". The radius of a 2 SM neutron star is not known accurately enough to make such a definitive statement. But it does appear 2 SM neutron star core pressure is much closer to (rho)(c^2)/3 than (rho)(c^2).

 

[PeterDonis]

it does appear 2 SM neutron star core pressure is much closer to (rho)(c^2)/3 than (rho)(c^2).

The pressure of relativistic matter in general will approach $\rho c^2 / 3$, not $\rho c^2$. IIRC the main relativity textbooks discuss this.

 

[PeterDonis]

[Moderator's Note: Moved thread to the relativity forum.]

 

[Bernie G]

The pressure of relativistic matter in general will approach $\rho c^2 / 3$, not $\rho c^2$. IIRC the main relativity textbooks discuss this.

http://pavi14.syr.edu/Talks/Thursday/RutledgePavi.pdf predicts a 2SM neutron star radius of only 9 km. It would be interesting to see his estimated core pressure and density and see what fraction of $\rho c^2$ his estimated core pressure is.

 

[Bernie G]

A NS isn’t a gas star but if you use the gas star formulas in Exercise 4.2 at http://www3.kis.uni-freiburg.de/~schliche/lectures_files/StEvol.pdf
for density = 15M/8πR^3 and gravitational core pressure = 15GM^2/16πR^4 , then using rho(c^2)/3 for pressure, the solution for 2 SM is 9 km. Maybe neutrons collapse at rho(c^2)/3.

 

[PeterDonis]

if you use the gas star formulas

These formulas look non-relativistic to me; a neutron star is not non-relativistic. Also, neutron star matter has a very different equation of state from the matter in an ordinary star.

 

[Bernie G]

These formulas look non-relativistic to me; a neutron star is not non-relativistic. Also, neutron star matter has a very different equation of state from the matter in an ordinary star.

My guess is a neutron star has pretty close to the density profile he is using. Yes the formulas are non-relativistic.

 

[PeterDonis]

My guess is a neutron star has pretty close to the density profile he is using.

You shouldn't guess; you should look at the actual math.

Yes the formulas are non-relativistic.

Then they won't apply to neutron stars, which are relativistic.

 

[Bernie G]

You shouldn't guess; you should look at the actual math.

Do you have a better approximation for density profile than 1 - (r^2)/(R^2) ?

 

[PeterDonis]

Do you have a better approximation for density profile than 1 - (r^2)/(R^2) ?

In most cases of physical interest, no closed-form expression for the density profile is known. You have to solve the differential equations numerically.

 

[Bernie G]

Anyway it appears the core pressure of a 2 SM neutron star is close to $\rho c^2 / 3$. A coincidence? And its interesting that if its radius is only 9 km that's about the size of its hypothetical photon sphere. My guess is neutron star mass is limited by core collapse instead of a surface event.

 

[PeterDonis]

it appears the core pressure of a 2 SM neutron star is close to ρc2/3\rho c^2 / 3. A coincidence?

No, that is expected based on the behavior of relativistic matter.

My guess is neutron star mass is limited by core collapse instead of a surface event.

I'm not sure what you mean by this.

 

[Bernie G]

"I'm not sure what you mean by this."

My thoughts are the largest pressure that can occur in nature could be $\rho c^2 / 3$ (a relativistic formula) and this is exceeded by the gravitational core pressure in a neutron star >2 SM. Above 2 SM some neutrons in the core collapse/disintegrate into charged quark type matter and radiation. Do you have any other alternative to what happens to a neutron when it collapses? In the NS this newly produced charged quark matter quickly recombines becoming neutrons, and the radiation escapes, for a net mass loss. Just my opinion.

 

[PeterDonis]

thoughts are the largest pressure that can occur in nature could be $\rho c^2 / 3$ (a relativistic formula)

Yes, this is correct for ordinary matter or radiation.

and this is exceeded by the gravitational core pressure in a neutron star >2 SM

No, this is impossible; see above.

Do you have any other alternative to what happens to a neutron when it collapses?

"Collapse" in this context does not necessarily mean "a neutron can no longer maintain its structure and turns into something else". It can mean simply "a neutron star can no longer support itself against its own gravity and collapses into a black hole". The latter can happen without the former happening.

Just my opinion.

PF is not for discussion of personal opinions. In areas that are not yet well understood, the best we can do is to recognize that all hypotheses are speculative and leave it at that.

 

[PeterDonis]

This topic has been sufficiently discussed. Thread closed.