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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 |
#2
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Schwarzschild Black Hole - any density?
"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). |
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Schwarzschild Black Hole - any density?
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 |
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Schwarzschild Black Hole - any density?
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 |
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Schwarzschild Black Hole - any density?
"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. |
#6
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Schwarzschild Black Hole - any density?
"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? |
#7
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Schwarzschild Black Hole - any density?
"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. |
#8
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Schwarzschild Black Hole - any density?
"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? |
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Schwarzschild Black Hole - any density?
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. |
#10
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Schwarzschild Black Hole - any density?
"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 |
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