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Space Forum / Astronomy / March 2007A Hollow Black Hole?
Yes, yes, they are dense and have a singularity. Well, we can't crack one open and have a look. But we can observe Neutron stars and if a Black Hole could be hollow you would expect to find a similar analogy in Neutron Stars. So here is the process. We know that just below the Chandrasekhar Limit a star will form a Neutron Star, above it forms a Black Hole. Way below the limit it just explodes in a supernova blast. But what happens if it begins to explode even though it has a great mass? And why wouldn't it begin to explode when the star collapses and everything inside heats up? So the inside explodes but is stifled by the collapsing mass. The momentum of the explosion is conserved in the form of angular momentum and the heat inside escapes in a huge stream of energy through some crack in the now super solid neutron shell - our lighthouse beam from which we can measure its rotational speed. A neutron star would have to rotate at an enormous speed to prevent further collapse or the internal pressure would have to be extremely great to hold the shell from collapsing or there would have to be some combination of the two. The reason why this scenario seems at all plausible is the discovery of extremely rapidly rotating Neutron Stars, well beyond what was thought to be the speed limit. See 'Fastest spinning star may have exotic heart' http://space.newscientist.com/article/dn11221?DCMP=NLC-nletter&nsref=dn11221 (Automatically posted to members of 'Physical Sciences' http://groups.yahoo.com/group/physical_sciences/ ) The rotational speed of this object is 1,122 rotations per second. Neutron Stars typically have a diameter of 10-15 kilometres. A little arithmetic tells me that the surface speed is between 32,248 and 52,873 km/s or less than 1/6 the speed of light - that is one wild ride :) Surely that speed is sufficient to support a hollow shell even in a neutron star - or is it? What speed would be necessary? There are some wonderful GR minds here at sci.physics.relativity - surely one of them can model such an object? Select a mass just below the Chandrasekhar Limit and a diameter typical of neutron stars of 10~15km. I understand the density of the neutron stars are all much the same, so one only needs to calculate the diameter of a solid neutron star and then increase the diameter to form a hollow cavity. Then calculate the required rotational speed to prevent the hollow cavity from being overwhelmed by the dense matter of the star. Is a rotational speed of 1,122 sufficient? Is the surface speed less than c? If a neutron star can do it then a hollow Black Hole can not be ruled out. Objections on aesthetic or philosophical grounds are of little value here - the hollow sphere should be modelled first, the required rotational speed calculated and checked against the highest possible speed for such objects, and then possible evolutionary paths to the formation of the object can be explored. Can anyone rise to this challenge? Of course if this issue has been considered before then please point us to it :)  SignatureKind Regards Robert Karl Stonjek > Yes, yes, they are dense and have a singularity. GR is not a quantum theory so we cannot analyse a black hole fully. If we ignore that quantum aspect, for an isolated black hole (which isn't accreting) all the mass is in the central singularity. That is a point of zero volume hence infinite density (in reality there might be some quantum limit to that) and outside that point the density is zero. > Well, we can't crack one > open and have a look. But we can observe Neutron stars and if a Black > Hole > could be hollow ... How can a point be hollow? That doen't even make sense. > ... We know that just below the Chandrasekhar Limit a > star will form a Neutron Star, above it forms a Black Hole. Way below the > limit it just explodes in a supernova blast. No, way below (like our Sun) it turns into a red giant and then a white dwarf, or even further below it is a brown dwarf. > But what happens if it begins to explode even though it has a great mass? > And why wouldn't it begin to explode when the star collapses and > everything > inside heats up? That's what happens, the star collapses, the outsides are blown out and in some cases the centre is compressed above the limit where a black hole forms. The details of supernovae vary with the type and the best thing you can do is to search the web for descriptions of the various processes. > The reason why this scenario seems at all plausible is the discovery of > extremely rapidly rotating Neutron Stars, well beyond what was thought to [quoted text clipped - 13 lines] > neutron > star - or is it? What speed would be necessary? Nothing could support a shell, the material at the poles is not moving and will collapse. The effect of rotation, like that of any star, will be to make the shape slightly oblate. > There are some wonderful GR minds here at sci.physics.relativity - surely > one of them can model such an object? Select a mass just below the > Chandrasekhar Limit and a diameter typical of neutron stars of 10~15km. I > understand the density of the neutron stars are all much the same, so one > only needs to calculate the diameter of a solid neutron star and then > increase the diameter to form a hollow cavity. Try calculating the pressure as a function of depth going down from the pole to the centre bearing in mind the density of material. > If a neutron star can do it then a hollow Black Hole can not be ruled out. > > Objections on aesthetic or philosophical grounds are of little value > here - Indeed, but the hollow neutron star is ruled out by hydrostatics and a hollow black hole is ruled out because a point has no volume. > Of course if this issue has been considered before then please point us to > it :) I doubt anyone has given the idea any thought at all, what you will find if you look is a lot of work trying to determine the "equation of state" for neutron stars. George > > Yes, yes, they are dense and have a singularity. > [quoted text clipped - 11 lines] > > How can a point be hollow? That doen't even make sense. A Schwarzschild Radius can be of any size, including a universe sized extension - there need not be a point in every case. A Black hole only needs to have an escape velocity of c, and a hollow sphere can have sufficient mass to curve space enough to qualify as a black hole. The assumption that all Black Holes have a singularity is based on the extrapolation of their evolution and ignores the possibility of high rotational speeds. > > But what happens if it begins to explode even though it has a great mass? > > And why wouldn't it begin to explode when the star collapses and [quoted text clipped - 11 lines] > > be > > the speed limit. See 'Fastest spinning star may have exotic heart' http://space.newscientist.com/article/dn11221?DCMP=NLC-nletter&nsref=dn11221 > > (Automatically posted to members of 'Physical Sciences' > > http://groups.yahoo.com/group/physical_sciences/ ) [quoted text clipped - 42 lines] > > George > A Schwarzschild Radius can be of any size, including a universe sized > extension - there need not be a point in every case. A Black hole only > needs to have an escape velocity of c, and a hollow sphere can have > sufficient mass to curve space enough to qualify as a black hole. No real material employing the known forces of nature in its structure can withstand the forces that obtain from gravitation below an event horizon. Any material that is not in a central singularity soon will be (for suitable values of "soon" that depend upon the overall size of the black hole). > The assumption that all Black Holes have a singularity is based on the > extrapolation of their evolution and ignores the possibility of high > rotational speeds. High rotational speeds are not sufficient to hold a shell of matter from collapsing inside an event horizon. The rotational speed of the matter would have to exceed the speed of light, and it would only help at the equator of the shell. > > A Schwarzschild Radius can be of any size, including a universe sized > > extension - there need not be a point in every case. A Black hole only [quoted text clipped - 17 lines] > speed of light, and it would only help at the equator of > the shell. Yes, we've killed off this one - question to freshman, ten minutes to explain why a black hole can't be hollow... >> > Yes, yes, they are dense and have a singularity. >> [quoted text clipped - 16 lines] > needs to have an escape velocity of c, and a hollow sphere can have > sufficient mass to curve space enough to qualify as a black hole. Let's draw a section of what you seem to be suggesting: |####| + A |####| B |####| ^ ^ ^ | | | | | | The centre The shell Points A and B are just inside and just outside the shell. The total mass enclosed by a concentric sphere passing through A is zero so that doen't produce a horizon so I suppose you are saying the Schwarzschild Radius is the distance from the centre to point B. Now as has been said, GR is subtely different from Newtonian gravity. In the latter, an object fired outwards from the surface of the shell could move past point B but could not escape and would fall back. That's not the case in GR. Let an object fall from some large distance starting nearly at rest. When it reaches point B heading for the centre, it's fre-fall speed will reach the speed of light. Between B and when it hits the shell, the speed exceeds that of light (in some suitable coordinate system!). If you try to fire something upwards at point B, it has to be launched at the speed of light relative to free-falling (inertial) material just to stay at point B. As you know from SR, you cannot move faster than the speed of light in any inertial frame, including that of the free-fall material as it passes you. The bottom line is that your shell material must move faster than the speed of light relative to free-fall material if it is to stay at a constant radius and that as we know is impossible in GR so the shell collapses. > The assumption that all Black Holes have a singularity is based on the > extrapolation of their evolution and ignores the possibility of high > rotational speeds. No, it is based on the impossibility of moving faster than the speed of light. Your shell material will inevitably fall towards the centre accelerating as it do so and the process has no end in GR so the ultimate fate is for the entire mass to be come a mathematical point at the centre. The total mass remains the same of course and so does the Schwarzschild Radius so the event horizon is a sphere passing through point B. Note that for a supermassive black hole, the acceleration at the horizon can be less than 1g, and in free fall you don't even feel that. You could fall towards one of those, pass the horizon and be as unaware of the event as someone on a ship passing below the horizon as seen by someone on a cliff some miles away. Andrew Hamilton's pages on black holes are excellent: http://casa.colorado.edu/~ajsh/schw.shtml Only the distortions he shows would tell you the horizon was behind you. George > GR is not a quantum theory so we cannot analyse a black > hole fully. If we ignore that quantum aspect, for an isolated > black hole (which isn't accreting) all the mass is in the > central singularity. That is a point of zero volume hence > infinite density (in reality there might be some quantum > limit to that) and outside that point the density is zero. My conception of the interior of a black hole is that the singularity is a mathematical limit, or extrapolation of what is actually happening, but is never actually reached. In my view, the matter falling into and forming the black hole (both the original collapsing star and any matter which falls in at a later time) is forever falling toward the center, becoming ever more compressed circumferentially but ever more stretched out (spaghettified!) radially. The ever-increasing density of the center part of the black hole causes the curvature of spacetime there to continually increase, so that in effect the gravity well is forever getting deeper. By some measure (relative to what, I don't know), I think it is increasing in depth at the speed of light. Of course, none of this has any implication for what an observer would see, even if the observer were inside the black hole relative to another observer farther out. The black hole is always just a featureless black hole. And in contrast to the original post and the main point of this thread, I'm ignoring rotation. -- Jeff, in Minneapolis The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? -- Stephen Hawking -- Ahmed Ouahi, Architect Best Regards! > > GR is not a quantum theory so we cannot analyse a black > > hole fully. If we ignore that quantum aspect, for an isolated [quoted text clipped - 25 lines] > > -- Jeff, in Minneapolis > A Schwarzschild Radius can be of any size, including a universe sized > extension - there need not be a point in every case. Hmmm. In the Schwarzschild manifold of GR, the horizon is nowhere near the entire universe -- the horizon is of finite "radius" while the universe of that particular manifold is spatially infinite. Now some people, yourself included, seem to think it is possible for a "Schwarzschild black hole" to inhabit our universe. Strictly speaking this simply is not possible, as the universe we inhabit is quite clearly not well modeled by the Schw. manifold (e.g. that manifold contains no stars, planets, or people). However it does seem likely that objects similar in exterior appearance to a Schw. black hole could inhabit our universe, though it is extremely unlikely -- Kerr, Neumann, and/or Reisner-Nordstrom black holes are vastly more likely (they have nonzero angular momentum and/or charge). > A Black hole only > needs to have an escape velocity of c, No. A black hole only needs a trapped surface. You are thinking in Newtonian mechanics (NM), not GR -- "escape velocity" does not really apply to black holes. The difference is: NM: a freefalling object traveling with less than the escape velocity can still travel outward, but must fall back; a rocket can escape with any velocity > 0 as long as it can accelerate sufficiently (including moving slower than escape velocity). GR: no object or light ray can travel outward from an event horizon, regardless of how strongly it can accelerate. A trapped surface is the local definition of an event horizon; it is a surface from which all light rays travel to only one side of the surface (i.e. none travel "outward"). This is MUCH more powerful than the escape velocity of NM. > and a hollow sphere can have > sufficient mass to curve space enough to qualify as a black hole. Yes, one can imagine a _collapsing_ hollow sphere that is massive enough to have a trapped surface outside. An observer inside would be unaware of the presence of the horizon or the inevitability of it collapsing in and crushing her (because there is a series of trapped surfaces traveling inward with local speed c so no warning could possibly reach her before they do). At least I'm pretty sure that is how the geometry of a collapsing spherical shell would work out; I do not know of any actual solution describing this. > The assumption that all Black Holes have a singularity is based on the > extrapolation of their evolution and ignores the possibility of high > rotational speeds. Hmmm. This is more a definition of what "black hole" means than any assumption. That is, all black hole manifolds in GR have some sort of singularity -- the presence of an event horizon is the defining characteristic of a black hole, and one of the singularity theorems states that the presence of a trapped surface (aka horizon) implies the presence of a singularity (loosely; there are additional caveats). Note, however, this is "presence" in the 4-d manifold, and for the case of a collapsing system there could be no singularity inside until the collapse is nearly complete -- that is, do not confuse "time in the manifold" with "time to an external analyst". Jeff Root said: > In my > view, the matter falling into and forming the black hole (both > the original collapsing star and any matter which falls in at > a later time) is forever falling toward the center, becoming > ever more compressed circumferentially but ever more > stretched out (spaghettified!) radially. This is NOT what happens in GR. In GR any timelike trajectory inside the event horizon of a Schw. black hole intersects the singularity at the center in finite proper time. Tom Roberts Tom Roberts replied to Jeff Root: > > In my view, the matter falling into and forming the black > > hole (both the original collapsing star and any matter which [quoted text clipped - 5 lines] > inside the event horizon of a Schw. black hole intersects the > singularity at the center in finite proper time. Can you show what the proper time would be for some simple case of a neutral particle free-falling straight in to a nonrotating stellar-mass black hole? Since I know that everything which falls into a black hole *is* stretched in the radial direction, can you also give a measure of that stretching for the test particle? Is it stretched only in a space dimension, or only in time, or both, or what? -- Jeff, in Minneapolis All political thinking for years past has been vitiated in the same way. People can foresee the future only when it coincides with their own wishes, and the most grossly obvious facts can be ignored when they are unwelcome. -- George Orwell -- Ahmed Ouahi, Architect Best Regards! > Tom Roberts replied to Jeff Root: > [quoted text clipped - 18 lines] > > -- Jeff, in Minneapolis > > A Schwarzschild Radius can be of any size, including a universe sized > > extension - there need not be a point in every case. Toom Roberts Said: > Hmmm. In the Schwarzschild manifold of GR, the horizon is nowhere near > the entire universe -- the horizon is of finite "radius" while the [quoted text clipped - 5 lines] > not well modeled by the Schw. manifold (e.g. that manifold contains no > stars, planets, or people). No, Tom, I don't think there is any chance that our universe could be a Schwarzschild black hole but I do consider a 'universe sized Schwarzschild black hole' which is quite different. Further, I am considering only the matter and not the space. It seems rather obvious that if our universe was something like a Schwarzschild black hole then it would necessarily be in the process of collapsing to that singularity you mention, though this could take many billions of years to happen. Even so, such a collapse would blueshift the light from distant stars and galaxies - indeed, it would be quite *opposite* to what we observe. That rules out such a structure from even a philosophical account of the universe. In short, the universe can not be both expanding and anything like a Schwarzschild black hole. The rotating shell died because of what should have been dead obvious to me in the first place - rotation does not prevent collapse at the poles... SignatureKind Regards Robert Karl Stonjek > > > A Schwarzschild Radius can be of any size, including a universe sized > > > extension - there need not be a point in every case. > > > Toom Roberts Said: The above was a typo - not making fun of anyone - sorry TOM. SignatureKind Regards Robert Karl Stonjek > Yes, yes, they are dense and have a singularity. Well, we can't crack one > open and have a look. But we can observe Neutron stars and if a Black Hole [quoted text clipped - 11 lines] > crack in the now super solid neutron shell - our lighthouse beam from which > we can measure its rotational speed. Explosive momentum is essentially radial, thus linear. Angular and linear momenta are conserved separately. There's no mechanism for converting one to the other. > A neutron star would have to rotate at an enormous speed to prevent further > collapse or the internal pressure would have to be extremely great to hold [quoted text clipped - 15 lines] > Surely that speed is sufficient to support a hollow shell even in a neutron > star - or is it? What speed would be necessary? A neutron star has not collapsed beyond forcing the electrons to combine with the protons. Neutron degeneracy pressure can resist further callapse up to some critical mass. Now, rapid rotation can certainly help by providing a centrifugal effect. This is equivalent to reducing the mass-energy density of the object. Ultimately, the ability of a shell to resist collapse depends upon the compressive strength of the material along with whatever forces are aiding it. Perhaps you are thinking that, if the outer shell were rotating and the interior material was not, then the shell could resist ultimate collapse while the interior headed towards black holedom. A couple of problems arise. First, the shell would be outside of the event horizon (the mass-energy density is lowered by the rotation of the shell). Second, the poles of the shell would not benefit from the rotation. The matter at the poles would end up collapsing. > There are some wonderful GR minds here at sci.physics.relativity - surely > one of them can model such an object? Select a mass just below the [quoted text clipped - 5 lines] > dense matter of the star. Is a rotational speed of 1,122 sufficient? Is > the surface speed less than c? If you increase the diameter of the object while maintaining the same amount of matter, the density will drop and you'll no longer be close to the Chandrasekhar limit. > If a neutron star can do it then a hollow Black Hole can not be ruled out. I take it that you're thinking of a rotating shell of matter (neutronium) spinning just below an event horizon and resisting collapse. As I pointed out above, the poles of the shell would be a problem -- the neutron degeneracy pressure would be insufficient to prevent them from collapsing and whole shell would be consumed. > Objections on aesthetic or philosophical grounds are of little value here - > the hollow sphere should be modelled first, the required rotational speed [quoted text clipped - 4 lines] > Of course if this issue has been considered before then please point us to > it :) > > Yes, yes, they are dense and have a singularity. Well, we can't crack one > > open and have a look. But we can observe Neutron stars and if a Black Hole [quoted text clipped - 24 lines] > > extremely rapidly rotating Neutron Stars, well beyond what was thought to be > > the speed limit. See 'Fastest spinning star may have exotic heart' http://space.newscientist.com/article/dn11221?DCMP=NLC-nletter&nsref=dn11221 > > (Automatically posted to members of 'Physical Sciences' > > http://groups.yahoo.com/group/physical_sciences/ ) [quoted text clipped - 48 lines] > pressure would be insufficient to prevent them from > collapsing and whole shell would be consumed. Ahh, the poles. Well, if ever a neutron donut is discovered, I thought of it first :) SignatureKind Regards Robert Karl Stonjek |
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