A Black Hole infinite dense singularity may exists in an empty space but in a discreate space-time are there boundaries and the highest density of the matter is like in atom nucleus. Gravity can not break a Pauli's exclusion principle. There are many examples in the astrophysics.
http://www.blackholes.int.pl

Doesn't the formation of a neutron star break atomic nuclei to create a greater density? Or have I misunderstood your post?

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The plural of "anecdote" is not "data".

The neutron star has similar density as an atom nuclei. There might be even 3 x 10^14 g/cm^3 http://instruct1.cit.cornell.edu/cou...o101/lec23.htm

So how do the particles avoid being in the same place at the same time if, in order to do so, they must exceed c because of gravity?

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My son is my universe.

After following you link I stumbled onto this paper by George F. Chapline. Chapline was formerly Feynman's teaching assistant and is now working at Lawrence Livermore.

Link: http://arxiv.org/abs/astro-ph/0503200

Here are what I thought were the salient points of Chapline's paper:

1)The picture of gravitational collapse provided by classical general relativity cannot be physically correct because it conflicts with ordinary quantum mechanics.

2)Classical black hole will not allow “atomic clocks” to be synchronized. QM requires universal time. He ciites Schrodinger’s equation and non-local correlations. Apparently, the non-local correlations require simultaneity. If I am recalling what I have read about them correctly, this is true.


3) Chapline talks about Godel’s Universe, which as far as anyone can tell, suffers from no mathematical flaws, and is based on GR, but allows travel into the past. In Godel’s model, time is essentially meaningless. This raises an issue I have pondered many times without ever arriving at a satisfactory solution. Is time really and truly connected to causality or is time something we use as a means to measure the duration of events and nothing else?

4) If one visualizes the vacuum as analogous to the ground state of a condensed matter system (Higgs Field?) and ordinary matter as analogous to excited states of this system (Higgs Boson?), then it follows that the atoms in the condensed matter system must move without collective rotation (Rules out Godel’s Universe?).


5) Concerning further problems with universal time, Chapline cites the work of John Synge. I found out that Synge did a lot of work on black holes, including the exploration of the interiors of such objects. Synge died in 1972 and was, apparently, a widely respected mathematician and physicists. I haven’t been able to find any of Synge’s papers on line.

6) Chapline says that matter falling into a black hole becomes “dark matter” and that such “dark stars” emit “dark energy”. From a layman’s point of view, none of this sounds to terribly far-fetched if he accepts GR and QM. It makes as much sense as they do.

I might add that the notion of a solid state universe has a philosophical appeal for me. I expect us to find out that the universe is an eternal and finite plenum in which everything is quantized.

I would like to point out that black holes can exist without the need for high densities, high pressures, high tidal forces, or anything equally spectacular. All you need is a very great total mass, and then the density can be quite low. Think of thousands of stars congregating together in a sphere no larger than the Solar System. There would still be empty space between them, and no need whatsoever to surpass the density of an atomic nucleus anywhere.

A star more massive then neutron star (3-7 solar masses) seems to collapse into a Black Hole denser then an atom nucleus. It have to has a diameter about 20 km and its surface rotate with speed of light - nobody has seen such a small and massive object.

This star will lose its mass down to 3 solar masses in an enormous radiation (Gamma Rays Bursts) or gain additonally mass from environment till it reaches minimum 7 solar masses and average neutron star density.

Close to speed of light and in very strong gravitational field particles are not spherical. In Magnetar Star atoms are long and thin like a needle. In this conditions a diameter of the neutron is different then on the Earth.

According to maximal concentration boundary , it is not possible to create a star under its Event Horizon in our reference frame, because of the time dilation.

It is true. There are supermassive Black Holes with millions and even billions solar masses with relatively low density.
More Mass - Larger Radius - less Density.
All this stars are very massive objects but with its Radius above an Event Horizon (more then Schwarzscild Radius) and there is no infinite dense singularity.
If two BHs come close and create a binary system they lose their energy by a gravitational field and change their centre of gravity. If they collide and merge (we see it as Short Gamma Rays Bursts) a new star will have a density less then a Neutron Star. I think , next generation of the telescopes will confirm this theory.http://www.blackholes.int.pl

The event horizion is not a solid surface and as such dosent relly rotate. If you were falling in and could survive the tidal forces, you would never even see the event horizion.
A neutron star has between 1.4 and ~3 solar mass. The originator stars may be heavier, but a neutron star cannot have between 3 and 4 solar mass. The limit on mass is a bit fuzzy because the conditions of the star can change the pressure in the star.
There are a few good candidates for a black hole where there is a massive compact object that should be identifiable as a neutron star, but there is not a neutron star there.
Black holes have been a part of theory since well before string theory, and they fit without string theory.

Thank you Spherical for remarks. It is helpful.
I think that a clasical Black Hole can't be created in our reference frame as distant observers, because a time dilation. A Dark Energy comes to us just from outside of our Observable Universe and it is different then Chapline idea.
I wrote it in my link http://www.blackholes.int.pl , just because Chapline do not belive in a clasical Black Hole with a singularity point.

"How many angels can dance on the head of a pin?"

Hum,
Assuming that blackholes exist,
the standard reply is that according to standard General Relativity there is no maximum density, so a star will collapse into a black hole.

This is only true if the star is really big, of course.
(A neutron star or example is formed when gravity overwhelms the exclusion principle so that electrons are merged with protons, forming neutrons...)

It should be noted that half-integer spin fermions obey the Pauli exclusion principle and so only exist as a single wave-function (matter) , while Integer-spin particles ( bosons) can be placed together in the same spot (they are the forces).
So it is only the fermions that need to be placed together, we can forget about bosons..

So normally, as was said, the Pauli exclusion principle will push Fermion particles apart.
However, if the gravity (space-time curve) is great enough then the force need to keep Fermions apart is overcome.
ie to stop from merging in a Blackhole, the Fermion will need to move faster than the speed of light to escape from another Fermion.

http://www.improbable.com/airchives/...angels-7-3.htm

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`Irony` actually does mean `metal like`...

Black Hole is it an idea that if star is more massive then 3 solar masses it might collapse under Event Horizon into a singularity point - it is an unobserved theory only. A Black Hole in our Milky Way has 150 millions km diameter, more massive BH has a diameter even more then Pluto orbit - it is density much less then neutron star.
If two Neutron Star colide and merge there is an enormous Gamma Rays Burst - this Rays are not bound under an Event Horizon.
If a matter falls down into a Black Hole (Quasar) a part of this matter is ejected in the jets just from the Black Hole - it is not bound under Event Horizon.
A better telescope in the future will show where comes from the Radio Emission of the Black Hole and we will know a structure of the Black Hole.
I would like in my link http://www.blackholes.int.pl ,to prove that Black Holes have an inside structure and it may expand.
This expansion is for distant observer very slowly but for an inside observer as fast as almost speed of light . It is because a time dilation.

In this case Fermions move near speed of light in very strong gravity - according Lorentz transformations there is time dilation and for us the distant observers they can not create a clasical Black Hole. It will be a Black Hole if we are just there as inner observer but it is an eternity for the outside Universe.

>>It will be a Black Hole if we are just there as inner observer but it is an eternity for the outside Universe.

Hum,
while i would generally agree with this,
the main point was to disprove the proposition that "Gravity can not break a Pauli's exclusion principle".

It is clear from my reply that the an electron (for example) cannot move faster than the speed of light to escape from another electron and so the two of them occupy (for all intents and purposes) the same space.

Local or distant the two fermions will merge into a black hole - Just because the distant observers is in a differant time frame does not mean they do not.

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`Irony` actually does mean `metal like`...

A massive star with more then 3 solar masses may theoretically collapse into a Black Hole with density higher then neutron star but practically there is a strong outburst of the energy and mass. A star with 7 solar masses may be stable with a density like neutron star.
The space-time has its boundaries and there is not possible free concentration of the matter. Very high concentration of the energy like micro Black Hole causes its immediately explosion.
We have no evidence that matter could be concentrated under Event Horizon or in a singularity point.

>>We have no evidence that matter could be concentrated under Event Horizon or in a singularity point.

Indeed, a Black Hole `infinite` dense singularity may not exist.

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`Irony` actually does mean `metal like`...

Yes, "Infinite Density" is "NOT" the infinty that is reached to create a 'singularity'!!!

Consider where the term "Infinite Density" came from.

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`Irony` actually does mean `metal like`...

The only way I can think of to achieve infinite density is to divide some given mass by a volume of zero. I can't imagine doing that to an electron, but I have been told that many physicists consider the electron to a bit of matter with zero volume, which would mean that it would have infinite density as well.

I'm like you, czeslaw, I have a hard time swallowing that one.

That does not mean the black hole doesn't exist!

It means that "Infinite Density", is a mis-nomer...if it actually was "Infinite",
it would swallow the whole universe!!!

The use of "Infinite Density" was orginally used in conjuction with the "Friedmann Naked Singularity", creating the whole universe!

Why, it was "ASSUMED", that if the whole universe was locked up inside the 'singularity', it "MUST" have "Infinite Density"!!!

Ever since then, both terms have been inseperable!

I have very little doubt that something very like a "black hole" ex