Why doesn't the pauli exclusion principle prevent the collapse of
matter in a black hole down to a singularity.

wrote:
Why doesn't the pauli exclusion principle prevent the collapse of
matter in a black hole down to a singularity.

In fact it does. BH's are BS.

Under enough pressure and mass the Neutron Star forces
create gamma ray emission, well observed by gamma ray
bursts.
Ken

Dear michalchik:

wrote in message
ups.com...
Why doesn't the pauli exclusion principle prevent
the collapse of matter in a black hole down to a
singularity.

"Gravitationally bound" is not a bound state to which Pauli
applies.

David A. Smith

N:dlzc D:aol T:com (dlzc) wrote:
Dear michalchik:

wrote in message
ups.com...
Why doesn't the pauli exclusion principle prevent
the collapse of matter in a black hole down to a
singularity.

"Gravitationally bound" is not a bound state to which Pauli
applies.
David A. Smith

Well that's in juxtaposition to my post (Tucker),
by implying 2 neutrons in the center of a n-star
may occupy the same space at the same time because
gravity did it.

NUTZ and Regards
Ken

wrote:
Why doesn't the pauli exclusion principle prevent the collapse of
matter in a black hole down to a singularity.

Here's an over-simplified semi-quantum/semi-classical description:

For neutrons in a neutron star, each neutron is confined to be inside
its surface (most of the time) by the nuclear forces between/among
neutrons. This gives them a specific momentum distribution which depends
primarily on the radius of the star's surface. If the surface is moved
inward, the momentum distribution must increase its maximum momentum,
because of the Fourier relationship between position and momentum (yes,
the same relationship that gives the Heisenberg uncertainty principle).
For neutron stars with total mass ~1.4 solar massses, a stable
equilibrium exists. But for larger neutron stars gravity pulls in the
surface enough so that the momentum distribution increases enough and
there are still enough momentum states so the neutrons can each have a
separate state -- this is unstable and gravity pulls the surface in
completely, all the way down to a point which becomes the singularity.

Oppenheimer (later of atomic bomb fame) wrote a paper on this in the
late 1930s, as did Chandresekhar and others. The ~1.4 solar mass limit
on neutron stars is known as the Chandresekhar limit.

It has been questioned whether or not there could be a smaller stable
equilibrium,possibly supported by "bare" quarks and/or gluons (rather
than neutrons). I believe the consensus currently is that there is no
smaller equilibrium, but AFAIK this is not firmly established.


Tom Roberts

:
Why doesn't the pauli exclusion principle prevent the collapse of
matter in a black hole down to a singularity.

The pressure from the neutron degeneracy in a neutron star prevents the
collapse of the neutron star (obviously). The pressure needed to prevent
the collapse can be obtained from an equation of state (which comes mostly
from extrapolations of nuclear equations of state to nuclear matter). Once
the pressure can no longer support the neutron star against gravitational
collapse, the matter will collapse until either something halts the
collapse or an event horizon forms around the collapsing matter. Once the
matter is inside the event horizon, I believe you can avoid the issue of
the exclusion principle for the following reason.

The radial direction (in a schwarzchild hole) is now timelike and the
t-direction is now spacelike, so there is not necessarily a ``lack of
spatial volume'' inside the black hole. The area covererd by the \theta and
\phi coordinates shrinks to zero as r - 0, but the t-coordinate becomes
infinite. Since the exclusion principle places a constraint on the wave
vectors (which correspond to the spatial directions that are now dt
and r^2 d\Omega^2), the exclusion principle is not necessarily an issue.

Since this just occured to me, I'll need to actually check to see how
much I might have gotten carried away and fibbed here, but it seems
reasonable that the actual interior spatial volume could be very large
even if the black hole appears quite small from the exterior.

At r = 0, the transverse dimensions are zero and the length of the
direction along t is infinite, so exactly what happens at the singu-
larity is speculative, but one might consider this applicable down to
the planck scale.

Bilge wrote:
:
Why doesn't the pauli exclusion principle prevent the collapse of
matter in a black hole down to a singularity.

The pressure from the neutron degeneracy in a neutron star prevents the
collapse of the neutron star (obviously). The pressure needed to prevent
the collapse can be obtained from an equation of state (which comes mostly
from extrapolations of nuclear equations of state to nuclear matter). Once
the pressure can no longer support the neutron star against gravitational
collapse, the matter will collapse until either something halts the
collapse or an event horizon forms around the collapsing matter. Once the
matter is inside the event horizon, I believe you can avoid the issue of
the exclusion principle for the following reason.

The radial direction (in a schwarzchild hole) is now timelike and the
t-direction is now spacelike, so there is not necessarily a ``lack of
spatial volume'' inside the black hole. The area covererd by the \theta and
\phi coordinates shrinks to zero as r - 0, but the t-coordinate becomes
infinite. Since the exclusion principle places a constraint on the wave
vectors (which correspond to the spatial directions that are now dt
and r^2 d\Omega^2), the exclusion principle is not necessarily an issue.

Knee-jerk

Suppose I set a CS at the center of an average n-star, relatively to
which we should expect the laws of physics - specifically Pauli's
Exclusion Principle - are valid. Then by astronomics, matter is added
to the n-stars surface, increasing it's mass in a continuous way.

I think we're safe to assume the pressure also increases but not
necessarily the density because incompressible fluid density does
NOT change linearily with pressure.

The assumption of an "incompressible fluid" is actually an application
of the PEP. However PEP allows two neutrons to change their relative
spins under sufficient containment to begin to occupy the same
location.
In that case each 2 neutrons change relative spin by 90 degrees for a
total of 180 relative, meaning they become relatively
neutron-antineutron
couples. At some point in the relative spin variation the neutrons
become
an attractive couple, and the usual neutron-antineutron decay occurs,
ultimately decaying to gamma rays.
The powerful gamma ray bursts would support that theory.

Regards
Ken S. Tucker
....

its
Incompressibility is relative. Everything is compressible. Electric
forces are saturated and "shielded" (balanced, rather) whereas gravital
forces are not, so the latter easily overcomes the former. The charges
are still excluded though. Tucker, stop making up antineutrons.

Ken S. Tucker wrote:
[...] because incompressible fluid density [...]

You just defined the problem away. In fact, the Pauli exclusion
principle does NOT cause a neutron star to be "incompressible". See my
earlier reply -- at some critical density further reduction of the
surface area does NOT reduce the number of states available to the
neutrons, and they can obey Pauli all the way down to zero volume.


In that case each 2 neutrons change relative spin by 90 degrees for a
total of 180 relative, meaning they become relatively
neutron-antineutron
couples.

You mean isospin, not spin. That's a WHOLE different beast.... But
isospin does not behave this way (neither does spin...).


At some point in the relative spin variation the neutrons
become
an attractive couple, and the usual neutron-antineutron decay occurs,
ultimately decaying to gamma rays.
The powerful gamma ray bursts would support that theory.

Nonsense. neutron-anitneutron annihilation has a Q value of ~1
GeV/gamma; gamma ray bursts have observed energies billions of times
that. And that is AFTER any redshift from either gravitation or
cosmology (because it is measured here on earth).


Tom Roberts

Tom Roberts wrote:
Ken S. Tucker wrote:
[...] because incompressible fluid density [...]

Quote out of context is immature.

You just defined the problem away. In fact, the Pauli exclusion
principle does NOT cause a neutron star to be "incompressible". See my
earlier reply -- at some critical density further reduction of the
surface area does NOT reduce the number of states available to the
neutrons, and they can obey Pauli all the way down to zero volume.

Tom, that's silly you got 2 neutrons in a zero volume, like two
same spin particles occupying the same point, and then claim
that's ok with PEP, then you have your own version of PEP.

Ken
....