Dear Neil,

In principle this could be a good idea if a Bose-Einstein would guarantee that you can get a very high density. But that is not the case because the Bose-Einstein condensate is the occupation of the fundamental state by many bosons and the state dosen't need to be localized in one point. For instance, the Cooper pairs of a superconductor are in the same state but they are not localized in one point.

It is true that the condensate of the bosons gives the idea that at low temperatures they are very localized and therefore with a great density, at least much higher if they were in a gass phase. But in any case the highest density is far of being contained in one sphere of their corresponding Schwarzschild radius. For instance, to introduce all the Moon mass in a sphere of 0.1 mm of radius. Could you imagine Moon condensate in such small particle? If you could get a condensate in such conditions thus you would obtain a black hole.

No, because the only property that matters is the mass, for neutral matter. Whatever the state of matter, if the mass exceeds a certain value, a region of spacetime is causally disconnected from the rest.

So Bose-Einstein condensation isn't a relevant property for black hole formation.

It's known that classical electromagnetic waves can lead to black hole formation: Article Black hole formation by incoming electromagnetic radiation

No, BE condensation is not associated with the formation of a black hole.

Dear Neil,

In principle this could be a good idea if a Bose-Einstein would guarantee that you can get a very high density. But that is not the case because the Bose-Einstein condensate is the occupation of the fundamental state by many bosons and the state dosen't need to be localized in one point. For instance, the Cooper pairs of a superconductor are in the same state but they are not localized in one point.

It is true that the condensate of the bosons gives the idea that at low temperatures they are very localized and therefore with a great density, at least much higher if they were in a gass phase. But in any case the highest density is far of being contained in one sphere of their corresponding Schwarzschild radius. For instance, to introduce all the Moon mass in a sphere of 0.1 mm of radius. Could you imagine Moon condensate in such small particle? If you could get a condensate in such conditions thus you would obtain a black hole.

Dear All,

thank you for your good points.

So are you saying the fact that the wave functions of bosons are allowed to overlap does not enable these particles to be drawn together than closer than fermions?

I'm assuming densities greater than atomic are prevented by Coulomb repulsion or electrons, and like wise for nuclear densities due to the repulsion from the charges on the quarks.

Would it therefore be possible to create densities greater than nuclear if fundamental particles with integer spin, mass and no charge were brought together in a condensate?

I know this is a bit of a hypothetical question, but the Z-boson is such a particle. In a condensate what might prevent this collapsing under its own gravity?

The overlap of the wavefunctions is irrelevant because it doesn't affect whether a black hole forms or not.

The reason no massive, point-like object, collapses to a naked singularity, is because gravitational interactions are irrelevant, when such particles can be identified.

When the backreaction can't be neglected, the description in terms of particles isn't appropriate.

Dear Neil,

Your idea is interesting:

So are you saying the fact that the wave functions of bosons are allowed to overlap does not enable these particles to be drawn together than closer than fermions?

The neutron stars transform in quark starts when the mass is great enough and finally collapse in a black hole.

What avoids that they collapse, before having three times the Sun mass, is the Pauli exclusion principle for fermions. Thus, giving that this doesn't apply to the bosons, you ask what prevents the collapse in boson condensate? Nothing, in the case of having bosons you would obtain earlier the black hole for a smaller mass of the star.

Another question is if you can get a very high density just using boson condensation.This is difficult to reach because you need to have a great number of bosons in the fundamental state. If you look for particles as photons or gravitons this is impossible because they have rest mass zero. The Z bosons are good candidates because they are very massive but only involved in weak interaction where the neutrinos play a fundamental role or the decay under neutral currents were working. In all that it knows this is far of being possible to get a great number of these particles in one stable state for forming a condensate.

On the other hand, notice that although the Pauli exclusion principle doesn't apply to the bosons, there is the uncertainty Heisenberg principle which prevents to localize the bosons with great rest mass providing them with great velocity. This tells you that this is not the best form to collapse bosons to form a gravitational singularity as the black holes.

Dear Daniel,

that was more or less what i was thinking, there is nothing like the Pauli exclusion principle to prevent further collapse with bosons, so collapse to high densities might happen at lower total mass.

But yes, the increase in the de Broglie wavelength with falling temperature does really go against getting the system to collapse under its own gravity. Something like the Scharzchild l radius being larger than the de Broglie wavelength sets the mass for collapse to be inversely proportional to the temperature.

So perhaps the scheme would be to forget the condensate, but just to put a large number of bosons together in a given place? The critical mass for self-collapse should be less than that for fermions, but lower for higher temperatures. So if it heats up during collapse, that may help, by reducing the de Broglie wavelength?

Dear Neil,

I agree with you. The problem is that most of the bosons are atoms or gauge bosons. The fundamental particles as electrons, protons, neutrons etc...are fermions and they are the important when we speak about big body like a star.

I don't see what is the problem related with the Bose-Einstein condensate with the de Broglie wavelength , notice that if the velocity or the mass increase this decreases. Obviously if you have a frozen state where p were zero then you would have difficulties but this not allowed by the uncertainty Planck principle.

Dear Daniel,

since the vector bosons dont stay around for very long, there would need to be perhaps a specific type of experiment to get many of them in the same place at once. As you say, having a particle with a large mass to start would help. I guess its all about getting as much energy density in the Schwarzchild radius as possible, perhaps more likely to happen if the matter were in the form of bosons?

Dear Neil,

You are right, the idea of bosons is good for obtaining higher density than with bosons. The difficulty is that most of the stable fundamental particles as electrons, protons or neutrons are fermions.

Sorry,

I have written bosons instead of fermions, although it is quite obvious, I rewrite well :

You are right, the idea of bosons is good for obtaining higher density than with fermions. The difficulty is that most of the stable fundamental particles as electrons, protons or neutrons are fermions.