Black Hole Formation: Fermion Pressure & Neutron Stars

[kent davidge]

I was reading about the pressure which is created when fermions are close of each other like in an electron gas, and I started thinking about what causes a black hole to form. Firstly, what happens when two fermions are forced to occupy the same place (and state)? By the exclusion principle I would say a anihilation would occur... but the resulting energy of this process will cause space-time to curve... Is it concise with what REALLY happens in the formation of black holes, with the neutrons (of the neutron star) being the fermions? (Sorry for my bad English.)

 

[Nugatory]

Is it understood what REALLY happens in the formation of black holes, with the neutrons (of the neutron star) being the fermions?

The quick answer is "No, we do not know what happens to the matter that collapses to form a black hole".

General relativity predicts that once the event horizon forms and we have a black hole, the matter will continue to collapse all way down to a single point. However, this prediction does not consider the possibility that quantum mechanical effects will come into play under the extreme conditions at the center of the collapsing mass, so it's unlikely that that's what really happens. But we also don't have a good theory for what these quantum mechanical effects might be, so we don't know what happens instead.

All of this is going on behind the event horizon, after the black hole has formed. The black hole forms as soon as the density is high enough that all the matter is inside the Schwarzschild radius.

 

[kent davidge]

The quick answer is "No, we do not know what happens to the matter that collapses to form a black hole".

General relativity predicts that once the event horizon forms and we have a black hole, the matter will continue to collapse all way down to a single point. However, this prediction does not consider the possibility that quantum mechanical effects will come into play under the extreme conditions at the center of the collapsing mass, so it's unlikely that that's what really happens. But we also don't have a good theory for what these quantum mechanical effects might be, so we don't know what happens instead.

All of this is going on behind the event horizon, after the black hole has formed. The black hole forms as soon as the density is high enough that all the matter is inside the Schwarzschild radius.

Oh ok. What would occur if two fermions were forced to occupy the same quantum-mechanical state? Has someone ever tried this? Even if no experiment has been made, what can we say based on theories?

 

[Drakkith]

Oh ok. What would occur if two fermions were forced to occupy the same quantum-mechanical state? Has someone ever tried this? Even if no experiment has been made, what can we say based on theories?

Fermions cannot occupy the same state. It is impossible.

 

[kent davidge]

Fermions cannot occupy the same state. It is impossible.

But what would happen if we try

 

[Drakkith]

But what would happen if we try

You and I are testing this fact even as we speak. The fact that you and all other matter does not fall into itself is because fermions cannot exist in the same state. For a more extreme example, just look at a white dwarf. They exist as they are because electron degeneracy pressure holds them up against their own gravity. This is a direct result of the inability of fermions to exist in the same state. An even more extreme example is a neutron star, where neutron degeneracy pressure holds the star up against gravity.

 

[kent davidge]

You and I are testing this fact even as we speak. The fact that you and all other matter does not fall into itself is because fermions cannot exist in the same state. For a more extreme example, just look at a white dwarf. They exist as they are because electron degeneracy pressure holds them up against their own gravity. This is a direct result of the inability of fermions to exist in the same state. An even more extreme example is a neutron star, where neutron degeneracy pressure holds the star up against gravity.

These are good examples, but the force responsible for this separation is limited... here is where my question arises... what would happen if gravity wins... By Nugatory #2, matter will collapse until reach a single point. What can we say about this process using the well-know laws of quantum-mechanics? (as nugatory mentioned, we don't have yet a quantum theory for this extreme situation, what I am asking is how can we analyze the process using the well-known laws of QM)

 

[Drakkith]

The only thing you can say is that quantum physics doesn't allow for fermions to occupy the same state. The conditions inside the black hole eventually get well beyond what we can currently measure and the laws of physics at this scale is unknown. Maybe the pauli exclusion principle breaks down somewhere, maybe it doesn't. We simply don't know.

 

[kent davidge]

The only thing you can say is that quantum physics doesn't allow for fermions to occupy the same state. The conditions inside the black hole eventually get well beyond what we can currently measure and the laws of physics at this scale is unknown. Maybe the pauli exclusion principle breaks down somewhere, maybe it doesn't. We simply don't know.

So the correct approach is to use General Relativity to analyze black holes formation instead of Quantum Mechanics?

 

[Cutter Ketch]

The same space does not mean the same state. I'm not saying anybody knows what happens in a black hole. I'm just saying it is a logical error to equate the same space with the same state.

On a more speculative note, I think that it may well be wrong to think that they occupy the same space. Spacetime gets warped to an infinity at the singularity. Does that mean that there is an infinity of time and space available?

 

[Nugatory]

So the correct approach is to use General Relativity to analyze black holes formation instead of Quantum Mechanics?

Yes, definitely. No significant quantum mechanical effects are involved in the formation of the black hole. These only show up in the neighborhood of the central singularity "well away from" the event horizon and "after" the black hole is formed (the scare-quotes are there because those phrases really aren't right for describing the geometry inside the event horizon, but unfortunately the English langiage doesn't have anything better).

The formation of a black hole is described by the Oppenheimer-Snyder solution to the Einstein field equations: http://grwiki.physics.ncsu.edu/wiki/Oppenheimer-Snyder_Collapse

 

[Nugatory]

On a more speculative note, I think that it may well be wrong to think that they occupy the same space. Spacetime gets warped to an infinity at the singularity. Does that mean that there is an infinity of time and space available?

No, it means that the equations have been derived under conditions that don't apply at the singularity, so they aren't expected to produce correct answers there and the infinite curvature they predict should not be taken too seriously. (It's very loosely analogous to the infinite electrical field that Coulomb's law $E=qC/r^2$ "predicts" when $r=0$. In that more familiar problem we understand that there aren't really infinite electric fields and that we shouldn't be setting $r=0$ in this equation).

 

[kent davidge]

Okay. I got it. Just one more question:

Maybe the pauli exclusion principle breaks down somewhere, maybe it doesn't. We simply don't know.

If matter is compressed into the singularity, then why is it not a obvious indication that the Exclusion Principle is violated, since singularity is a unique point in space-time?

 

[rootone]

The appearance of a singularity in the equations is generally taken as a sign that physics beyond what GR predicts must be happening.
Not as a prediction that an infinitely dense object should actually exist inside a black hole.
Quantum effects are the obvious candidate, inducing some kind of phase change of the infalling material.
However we don't even have a good theory yet for what those effects could be.

 

[kent davidge]

The appearance of a singularity in the equations is generally taken as a sign that physics beyond what GR predicts must be happening.
Not as a prediction that an infinitely dense object should actually exist inside a black hole.
Quantum effects are the obvious candidate, inducing some kind of phase change of the infalling material.
However we don't even have a good theory yet for what those effects could be.

Thanks for your answer