Schwarzschild Black Hole - any density?

I have mentioned elsewhere that the Schwarzschild Black Hole can be of any
density, as that was my long time assumption (I assumed that this was common
knowledge and an accepted concept). But there seems to be some opposition
to this.

Consider a low density spatial extension with average density of
10-29g/cm^2. According to the Schwarzschild radius equation
r=(3c^2/8Gdpi)^.5 the radius should be 13.4022 Billion light years, total
mass of 8.5395^52kg.

We would expect to see objects close to the event horizon cascade toward the
centre under the influence of the gravitational force (curvature of space)
of all that accumulated mass, unless the entire Black Hole is rotating at a
sufficiently high speed or some force counter to the gravitational force,
such as dark energy, prevents the collapse.

We can also consider a magically 'just formed' Schwarzschild Black Hole that
has not begun to collapse just yet. The bottom line is that, given enough
mass, a Schwarzschild Black Hole can form.

I don't see where the singularity fits in to this type of Black Hole. A
relative singularity may be observed at some point near the centre by an
observer near the event horizon, but as one approaches the centre one would
find no such singularity. We can track part of this illusion by noting the
time dilation at various points from the event horizon to the centre. An
observer near the event horizon notes that clocks near the centre seem to
have stopped completely. But observers near the centre notice nothing
unusual about their own clocks but note that clocks near the event horizon
are running almost infinitely faster than their own.

But back to my original point - the simple math for a Schwarzschild Black
Hole, r=(3c^2/8Gdpi)^.5, indicates that a Black Hole can form from matter of
any density. The escape velocity, by the same math, is c, which is what we
expect of any Black Hole.

I think where some General Relativists have difficulty with this concept is
that they want all spacetime curvature to be actual and not relative. Thus
in a spatial extension many times greater than the Schwarzschild Radius they
see no Black Hole form, even though the math says that one does form but
only relative to the observers position in space ie two observers spatially
separate will observe Black Holes in different places, possibly encompassing
the other observer.

One important component of spacetime is time, and we know from SR just how
relative time can be. But can a Black Hole form which is not a Black Hole
independent of the observer ie could there be a Black Hole at some point in
space according to the measurements and observations made by one observer
but not another? I say yes.

--
Kind Regards
Robert Karl Stonjek

"Robert Karl Stonjek" wrote in message
...
I have mentioned elsewhere that the Schwarzschild Black Hole can be of any
density, as that was my long time assumption (I assumed that this was common
knowledge and an accepted concept). But there seems to be some opposition
to this.

Consider a low density spatial extension with average density of
10-29g/cm^2. According to the Schwarzschild radius equation
r=(3c^2/8Gdpi)^.5 the radius should be 13.4022 Billion light years, total
mass of 8.5395^52kg.

We would expect to see objects close to the event horizon cascade toward the
centre under the influence of the gravitational force (curvature of space)
of all that accumulated mass, unless the entire Black Hole is rotating at a
sufficiently high speed or some force counter to the gravitational force,
such as dark energy, prevents the collapse.

We can also consider a magically 'just formed' Schwarzschild Black Hole that
has not begun to collapse just yet. The bottom line is that, given enough
mass, a Schwarzschild Black Hole can form.

I don't see where the singularity fits in to this type of Black Hole.

A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

An observer sitting outside the mass distribution would see
a black hole with an event horizon, and would be able to
observe nothing of the internals. Since a spherical
distribution of matter behaves as a point mass to the
external observer, it behaves to him as though all the mass
were concentrated at a singularity. He would calculate
(but could not observe) that all of the matter inside,
regardless of its starting distribution, must collapse to a
singularity in a finite time.

However, an observer within the body would note that all
of the matter was heading inevitably towards the center,
that is, the mass distribution is collapsing. As it does
so the density rises and the boundary of his observable
universe collapses too. He is headed irresistably toward
the center along with everything else, and at some point
the density interior to his location will be sufficient for
him to observe an event horizon below him, one that is
growing as matter is falling in. Eventually this growing
event horizon will grow to meet the event horizon that the
external observer sees; the space within this horizon will
be devoid of matter save for the singularity at the center
(ignoring spontaneous particle pair generation).

Robert Karl Stonjek wrote:
[...]

A Schwarzschild black hole has density=0 EVERYWHERE and EVERYWHEN. That
is, it is a vacuum solution of the Einstein field equation.

A Schw. black hole has a central singularity which is characterized by a
constant M, and outside its horizon it behaves pretty much like an
object with mass M. But there is actually no mass anywhere.

Like so many around here, you really should learn something about the
subject before attempting to write about it. shrug


Tom Roberts

Greg Neill wrote:
A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

This is only true for densities above a critical density (which depends
on the size of the matter distribution). For instance, there's no
expectation that earth or sun must collapse. But a star well over the
Chandrasekhar limit (~1.5 solar masses) must collapse, unless it sheds
enough mass to get below the limit. That is a limit on mass, not density.


Tom Roberts

"Tom Roberts" wrote in message
t...
Greg Neill wrote:
A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

This is only true for densities above a critical density (which depends
on the size of the matter distribution). For instance, there's no
expectation that earth or sun must collapse. But a star well over the
Chandrasekhar limit (~1.5 solar masses) must collapse, unless it sheds
enough mass to get below the limit. That is a limit on mass, not density.

I was referring, of course, to matter unsupported by
other means such as electromagnetic forces as you
find in condensed matter. But you are correct in
that I should have been more specific.

"Greg Neill" wrote in message
m...
"Robert Karl Stonjek" wrote in message
...
I have mentioned elsewhere that the Schwarzschild Black Hole can be of
any
density, as that was my long time assumption (I assumed that this was
common
knowledge and an accepted concept). But there seems to be some
opposition
to this.

Consider a low density spatial extension with average density of
10-29g/cm^2. According to the Schwarzschild radius equation
r=(3c^2/8Gdpi)^.5 the radius should be 13.4022 Billion light years, total
mass of 8.5395^52kg.

We would expect to see objects close to the event horizon cascade toward
the
centre under the influence of the gravitational force (curvature of
space)
of all that accumulated mass, unless the entire Black Hole is rotating at
a
sufficiently high speed or some force counter to the gravitational force,
such as dark energy, prevents the collapse.

We can also consider a magically 'just formed' Schwarzschild Black Hole
that
has not begun to collapse just yet. The bottom line is that, given
enough
mass, a Schwarzschild Black Hole can form.

I don't see where the singularity fits in to this type of Black Hole.

A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

An observer sitting outside the mass distribution would see
a black hole with an event horizon, and would be able to
observe nothing of the internals. Since a spherical
distribution of matter behaves as a point mass to the
external observer, it behaves to him as though all the mass
were concentrated at a singularity. He would calculate
(but could not observe) that all of the matter inside,
regardless of its starting distribution, must collapse to a
singularity in a finite time.

However, an observer within the body would note that all
of the matter was heading inevitably towards the center,
that is, the mass distribution is collapsing. As it does
so the density rises and the boundary of his observable
universe collapses too. He is headed irresistably toward
the center along with everything else,

Maybe; maybe not. I can't see why a body couldn't be in an orbit around the
central mass, but lie within the event horizon. I can't even see why it
couldn't just be held up way above the central singularity by some kind of
scaffolding arrangement. (Assuming a really, really strong scaffold).

Nor am I convinced that the observable Universe for somebody within the
event horizon is constrained by the event horizon - matter has no problem
falling into the hole, and from the perspective of an observer inside the
event horizon this actually occurs - they can see matter and photons falling
through the event horizon.

and at some point
the density interior to his location will be sufficient for
him to observe an event horizon below him, one that is
growing as matter is falling in. Eventually this growing
event horizon will grow to meet the event horizon that the
external observer sees; the space within this horizon will
be devoid of matter save for the singularity at the center
(ignoring spontaneous particle pair generation).



Are you saying that within the black hole there may be one or more regions
that form a black hole within the black hole? On the face of it, this
appears possible (I have never really considered it before), but I can't see
why the singularities around the little black holes should necessarily
increase until they merge together to form a single black hole with the same
event horizon as the system as a whole.

Nor can I see why the matter inside a black hole should collapse to a
"single point". Apart from anything else, the Pauli exclusion principle
would seem to make this impossible if the black hole contains 3 or more
electrons. If all matter was made up of objects with no physical dimensions
(eg point masses), and they were allowed to occupy the same piece of space,
and they had no interactions other than gravity, and they had no angular
momentum, then, yes, they would collapse to a point. At least one of these
is impossible even in in principle (zero dimensions, due to Heisenberg).

Maybe I am misunderstanding your argument?

"Peter Webb" wrote in message
u...

"Greg Neill" wrote in message
m...
"Robert Karl Stonjek" wrote in message
...
I have mentioned elsewhere that the Schwarzschild Black Hole can be of
any
density, as that was my long time assumption (I assumed that this was
common
knowledge and an accepted concept). But there seems to be some
opposition
to this.

Consider a low density spatial extension with average density of
10-29g/cm^2. According to the Schwarzschild radius equation
r=(3c^2/8Gdpi)^.5 the radius should be 13.4022 Billion light years, total
mass of 8.5395^52kg.

We would expect to see objects close to the event horizon cascade toward
the
centre under the influence of the gravitational force (curvature of
space)
of all that accumulated mass, unless the entire Black Hole is rotating at
a
sufficiently high speed or some force counter to the gravitational force,
such as dark energy, prevents the collapse.

We can also consider a magically 'just formed' Schwarzschild Black Hole
that
has not begun to collapse just yet. The bottom line is that, given
enough
mass, a Schwarzschild Black Hole can form.

I don't see where the singularity fits in to this type of Black Hole.

A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

An observer sitting outside the mass distribution would see
a black hole with an event horizon, and would be able to
observe nothing of the internals. Since a spherical
distribution of matter behaves as a point mass to the
external observer, it behaves to him as though all the mass
were concentrated at a singularity. He would calculate
(but could not observe) that all of the matter inside,
regardless of its starting distribution, must collapse to a
singularity in a finite time.

However, an observer within the body would note that all
of the matter was heading inevitably towards the center,
that is, the mass distribution is collapsing. As it does
so the density rises and the boundary of his observable
universe collapses too. He is headed irresistably toward
the center along with everything else,

Maybe; maybe not. I can't see why a body couldn't be in an orbit around the
central mass, but lie within the event horizon. I can't even see why it
couldn't just be held up way above the central singularity by some kind of
scaffolding arrangement. (Assuming a really, really strong scaffold).

The reason is, according to our best theory of space
and gravity, within an event horizon all trajectories
must lead to a central singularity. The density of
the mass-energy curves the space in such a way that
this is so. Further, the force of gravity must
eventually overcome all other forces. This is due
to the fact that gravity is, without exception, a
strictly attractive force; there aren't positive and
negative gravitational charges that can cancel. So
there is ultimately nothing that can withstand the
attraction and everything must collapse.


Nor am I convinced that the observable Universe for somebody within the
event horizon is constrained by the event horizon - matter has no problem
falling into the hole, and from the perspective of an observer inside the
event horizon this actually occurs - they can see matter and photons falling
through the event horizon.

It is constrained in the sense that there is no way to
reach the event horizon from within. Things can fall in,
but nothing can move in any direction that leads anywhere
but towards the singularity.


and at some point
the density interior to his location will be sufficient for
him to observe an event horizon below him, one that is
growing as matter is falling in. Eventually this growing
event horizon will grow to meet the event horizon that the
external observer sees; the space within this horizon will
be devoid of matter save for the singularity at the center
(ignoring spontaneous particle pair generation).



Are you saying that within the black hole there may be one or more regions
that form a black hole within the black hole? On the face of it, this
appears possible (I have never really considered it before), but I can't see
why the singularities around the little black holes should necessarily
increase until they merge together to form a single black hole with the same
event horizon as the system as a whole.

The black hole will accrete matter (including other black
holes) and grow in size until all of the matter within the
original black hole is within a single singularity. This
is because there can be no escape from the original, and
everything inside must collapse.


Nor can I see why the matter inside a black hole should collapse to a
"single point". Apart from anything else, the Pauli exclusion principle
would seem to make this impossible if the black hole contains 3 or more
electrons. If all matter was made up of objects with no physical dimensions
(eg point masses), and they were allowed to occupy the same piece of space,
and they had no interactions other than gravity, and they had no angular
momentum, then, yes, they would collapse to a point. At least one of these
is impossible even in in principle (zero dimensions, due to Heisenberg).

Maybe I am misunderstanding your argument?

The Pauli Exclusion Principle is also eventually overcome
by gravity. The pressure that resists collapse due to the PEP
is called electron degeneracy pressure, and for a mass greater
than the Chandrasekar Limit (about 1.44 solar masses), it is
not able to prevent gravitational collapse.

"Greg Neill" wrote in message
m...
"Peter Webb" wrote in message
u...

"Greg Neill" wrote in message
m...
"Robert Karl Stonjek" wrote in message
...
I have mentioned elsewhere that the Schwarzschild Black Hole can be of
any
density, as that was my long time assumption (I assumed that this was
common
knowledge and an accepted concept). But there seems to be some
opposition
to this.

Consider a low density spatial extension with average density of
10-29g/cm^2. According to the Schwarzschild radius equation
r=(3c^2/8Gdpi)^.5 the radius should be 13.4022 Billion light years,
total
mass of 8.5395^52kg.

We would expect to see objects close to the event horizon cascade
toward
the
centre under the influence of the gravitational force (curvature of
space)
of all that accumulated mass, unless the entire Black Hole is rotating
at
a
sufficiently high speed or some force counter to the gravitational
force,
such as dark energy, prevents the collapse.

We can also consider a magically 'just formed' Schwarzschild Black
Hole
that
has not begun to collapse just yet. The bottom line is that, given
enough
mass, a Schwarzschild Black Hole can form.

I don't see where the singularity fits in to this type of Black Hole.

A motionless distribution of matter that is not infinite
in extent cannot remain static -- it must collapse.

An observer sitting outside the mass distribution would see
a black hole with an event horizon, and would be able to
observe nothing of the internals. Since a spherical
distribution of matter behaves as a point mass to the
external observer, it behaves to him as though all the mass
were concentrated at a singularity. He would calculate
(but could not observe) that all of the matter inside,
regardless of its starting distribution, must collapse to a
singularity in a finite time.

However, an observer within the body would note that all
of the matter was heading inevitably towards the center,
that is, the mass distribution is collapsing. As it does
so the density rises and the boundary of his observable
universe collapses too. He is headed irresistably toward
the center along with everything else,

Maybe; maybe not. I can't see why a body couldn't be in an orbit around
the
central mass, but lie within the event horizon. I can't even see why it
couldn't just be held up way above the central singularity by some kind
of
scaffolding arrangement. (Assuming a really, really strong scaffold).

The reason is, according to our best theory of space
and gravity, within an event horizon all trajectories
must lead to a central singularity. The density of
the mass-energy curves the space in such a way that
this is so. Further, the force of gravity must
eventually overcome all other forces. This is due
to the fact that gravity is, without exception, a
strictly attractive force; there aren't positive and
negative gravitational charges that can cancel. So
there is ultimately nothing that can withstand the
attraction and everything must collapse.


Why must gravity overcome all other forces?

Imagine a black hole the size of the Universe (as indeed it could be, if its
density exceeds that of the Schwarshild density). Why are you so sure that
everything in it must eventually collapse to a single point?


Nor am I convinced that the observable Universe for somebody within the
event horizon is constrained by the event horizon - matter has no problem
falling into the hole, and from the perspective of an observer inside the
event horizon this actually occurs - they can see matter and photons
falling
through the event horizon.

It is constrained in the sense that there is no way to
reach the event horizon from within. Things can fall in,
but nothing can move in any direction that leads anywhere
but towards the singularity.


and at some point
the density interior to his location will be sufficient for
him to observe an event horizon below him, one that is
growing as matter is falling in. Eventually this growing
event horizon will grow to meet the event horizon that the
external observer sees; the space within this horizon will
be devoid of matter save for the singularity at the center
(ignoring spontaneous particle pair generation).



Are you saying that within the black hole there may be one or more
regions
that form a black hole within the black hole? On the face of it, this
appears possible (I have never really considered it before), but I can't
see
why the singularities around the little black holes should necessarily
increase until they merge together to form a single black hole with the
same
event horizon as the system as a whole.

The black hole will accrete matter (including other black
holes) and grow in size until all of the matter within the
original black hole is within a single singularity. This
is because there can be no escape from the original, and
everything inside must collapse.


Collapse to a point? Why?


Nor can I see why the matter inside a black hole should collapse to a
"single point". Apart from anything else, the Pauli exclusion principle
would seem to make this impossible if the black hole contains 3 or more
electrons. If all matter was made up of objects with no physical
dimensions
(eg point masses), and they were allowed to occupy the same piece of
space,
and they had no interactions other than gravity, and they had no angular
momentum, then, yes, they would collapse to a point. At least one of
these
is impossible even in in principle (zero dimensions, due to Heisenberg).

Maybe I am misunderstanding your argument?

The Pauli Exclusion Principle is also eventually overcome
by gravity. The pressure that resists collapse due to the PEP
is called electron degeneracy pressure, and for a mass greater
than the Chandrasekar Limit (about 1.44 solar masses), it is
not able to prevent gravitational collapse.


Sure, its unable to prevent a black hole forming, but it is certainly
sufficient to prevent the collapse into a single point. Schwarzshild's
solutions to GR were derived in 1914-1918 (while he was in the trenches) and
published in about 1920 (I think) - long before the Pauli exclusion
principle was known. It played no part in Schhwarshild's mathematics.

The Pauli exclusion principle plays no direct part in the formation of a
black hole - indeed, there is no force which can prevent the collapse into a
black hole if the density is high enough.

It does have a huge effect on what happens within the black hole, and
specifically if all of the matter inside a black hole will collapse to a
single point. It can't, due to the Pauli exclusion principle. Or don't you
believe that the basic rules of QM apply inside a black hole? If not, why
not?

On Mar 24, 8:57 am, Tom Roberts wrote:

This is only true for densities above a critical density (which depends
on the size of the matter distribution). For instance, there's no
expectation that earth or sun must collapse. But a star well over the
Chandrasekhar limit (~1.5 solar masses) must collapse, unless it sheds
enough mass to get below the limit. That is a limit on mass, not density.

As I understand it, in order for the type Ia supernova to occur, it
must be a neutron star siphoning mass from some external source most
likely from a companion start. A neutron star has a very small
volume. So, the electron degeneracy will definitely occur if the
added mass to this neutron star reaches a critical limit --- the
Chandrasekhar mass. However, other stars, starting out with larger
volume and not necessarily neutron stars, are not bound by this 1.5
solar mass threshold.

"Peter Webb" wrote in message
u...

"Greg Neill" wrote in message
m...

[snip]

The reason is, according to our best theory of space
and gravity, within an event horizon all trajectories
must lead to a central singularity. The density of
the mass-energy curves the space in such a way that
this is so. Further, the force of gravity must
eventually overcome all other forces. This is due
to the fact that gravity is, without exception, a
strictly attractive force; there aren't positive and
negative gravitational charges that can cancel. So
there is ultimately nothing that can withstand the
attraction and everything must collapse.


Why must gravity overcome all other forces?

See above. Gravity is strictly attractive, and the
gravitational force can grow without bounds once
electron degeneracy pressure is overcome -- there
is no other force (that we know of) that matter
produces that can hold against it.


Imagine a black hole the size of the Universe (as indeed it could be, if its
density exceeds that of the Schwarshild density). Why are you so sure that
everything in it must eventually collapse to a single point?

Because that's what the physics of General Relativity
says will happen. Now GR could be wrong, but so far
there has never been an empirical observation that
has contradicted it in the least.

[snip]


The black hole will accrete matter (including other black
holes) and grow in size until all of the matter within the
original black hole is within a single singularity. This
is because there can be no escape from the original, and
everything inside must collapse.


Collapse to a point? Why?

Again, see above.



Nor can I see why the matter inside a black hole should collapse to a
"single point". Apart from anything else, the Pauli exclusion principle
would seem to make this impossible if the black hole contains 3 or more
electrons. If all matter was made up of objects with no physical
dimensions
(eg point masses), and they were allowed to occupy the same piece of
space,
and they had no interactions other than gravity, and they had no angular
momentum, then, yes, they would collapse to a point. At least one of
these
is impossible even in in principle (zero dimensions, due to Heisenberg).

Maybe I am misunderstanding your argument?

The Pauli Exclusion Principle is also eventually overcome
by gravity. The pressure that resists collapse due to the PEP
is called electron degeneracy pressure, and for a mass greater
than the Chandrasekar Limit (about 1.44 solar masses), it is
not able to prevent gravitational collapse.


Sure, its unable to prevent a black hole forming, but it is certainly
sufficient to prevent the collapse into a single point.

No! That's the whole point (pardon the pun). The
electron degeneracy pressure is overcome for a mass
concentration that exceeds the Chandrasekar limit.
The result will be a body composed of degenerate matter,
neutronium if the total mass is not too large. Add a
bit more mass and you overcome the degeneracy pressure
of the neutrons too (Tolmann-Oppenheimer-Volkoff limit,
analogous to the Chandrasekar limit). And, you can keep
on adding mass to exceed any conceivable limit of
opposing forces that might arrise beyond that point (say
quark degeneracy pressure, if it exists).


Schwarzshild's
solutions to GR were derived in 1914-1918 (while he was in the trenches) and
published in about 1920 (I think) - long before the Pauli exclusion
principle was known. It played no part in Schhwarshild's mathematics.

The Pauli exclusion principle plays no direct part in the formation of a
black hole - indeed, there is no force which can prevent the collapse into a
black hole if the density is high enough.

It does have a huge effect on what happens within the black hole, and
specifically if all of the matter inside a black hole will collapse to a
single point. It can't, due to the Pauli exclusion principle. Or don't you
believe that the basic rules of QM apply inside a black hole? If not, why
not?

The Pauli Exclusion Principle has limits regarding the amount
of force it can support. Beyond a certain point it ceases
to keep electrons with the same quantum numbers apart. See,
for example,

http://en.wikipedia.org/wiki/Electro...eracy_pressure