Black Holes and Degenerate Pressure

[lavinia]

Naive reading on the web says that stellar collapse is halted by quantum mechanical processes called "degenerate pressures" that arise when gravity tries to force fermions such as electrons or neutrons into the same quantum state. White dwarfs are propped up by electrons, neutron stars by neutrons, and it is speculated that other quantum mechanical plasmas may stabilize larger collapsing stars e.g quark plasmas. See for instance the Wikipedia articles on White Dwarfs and Neutron Stars. Also the Hubble telescope seems to have detected evidence of an anomalous neutron star that might really be a quark star.

From this it seems that matter tries to do its best to resist gravitational crunch but at some point gives up the battle. Why is this? Is it that beyond a certain limit there are no longer any more types of elementary particles that can counter stellar collapse? Or is is just that no matter what goes on in the quantum world General Relativity says a singularity is inevitable if the collapsing star is big enough? It seems a bit peculiar that Relativity predicts a singularity without any reference whatsoever to these quantum pressures.

Finally, as the singularity forms what happens to matter on its way down? Does it go through a series of stages of attempted resistance first say forming an electron plasma , then a neutron, then perhaps a quark and then others or is the process completely different?

 

[phyzguy]

One way to look at it is that as the material becomes more compressed, it gets denser and stiffer. This means the speed of sound increases. The speed of sound in neutron stars is estimated to be about 2/3 the speed of light. So matter cannot get much denser and stiffer than neutron star matter or the speed of sound would exceed the speed of light, which relativity says is impossible. So even if we do not know the details of matter interactions at these extremely high pressures and densities, we know that a body much larger than a neutron star cannot resist gravitational collapse. I'm not sure if we know exactly where this limit is (where no material could resist collapse, no matter how strong, or the speed of sound in the material would exceed the speed of light), but it is somewhere around 3-5 times the mass of the sun.

 

[lavinia]

One way to look at it is that as the material becomes more compressed, it gets denser and stiffer. This means the speed of sound increases. The speed of sound in neutron stars is estimated to be about 2/3 the speed of light. So matter cannot get much denser and stiffer than neutron star matter or the speed of sound would exceed the speed of light, which relativity says is impossible. So even if we do not know the details of matter interactions at these extremely high pressures and densities, we know that a body much larger than a neutron star cannot resist gravitational collapse. I'm not sure if we know exactly where this limit is (where no material could resist collapse, no matter how strong, or the speed of sound in the material would exceed the speed of light), but it is somewhere around 3-5 times the mass of the sun.

OK. That makes sense from the point of view of Relativity. But what about the Pauli Exclusion Principle? Does it just stop working?

 

[phyzguy]

OK. That makes sense from the point of view of Relativity. But what about the Pauli Exclusion Principle? Does it just stop working?

I don't think anyone knows. If we could answer questions like that, we would have a working theory of quantum gravity, which we don't have. Others may have a better answer.

 

[dendros]

Another possibility is that beyond a certain threshold, the collapsed matter's particles becomes bosonic.

 

[nikkkom]

OK. That makes sense from the point of view of Relativity. But what about the Pauli Exclusion Principle? Does it just stop working?

Pauli exclusion principle does not make it absolutely impossible to cram more particles into a fixed volume. It only requires that every new added particle must have a different state from all other already present particles. Which usually means it needs to have higher energy. Thus, a newly added particle needs to be moving faster. (Which, in turn, makes it exert pressure, causing "degenerate pressure").

Since it is always possible to have higher energy (possible energy levels are not bounded from above), neutron star can become denser and denser as matter is added to it. (in fact, calculations show that it even _shrinks_, it does not stay the same size). At some point it becomes a black hole. As matter collapses while BH is forming, even below event horizon, Pauli exclusion principle still works: particles go to higher and higher energy levels.

The point of singularity is, of course, problematic, because there ehergy of particles will go to infinity.