Black holes and whether General Relativity views light as a ballistic particle?

[Boffin]

A. See my questions below. First, here is some information from the book “Black Holes and Time Warps” by Kip Thorne. So far this is the best reference book I can find on the original thinking of black holes.

1. Pg 122 Very compact stars were theorized to occur way back in 1783 by John Michell on the basis that light was a particle and there would be an escape velocity.
2. Pg 123 Pierre Laplace also supported the idea of dark stars in the second 1799 edition of his book Le Systeme du Monde. But in the third printing he deleted reference to it because Thomas Young’s theories that light was a wave had gained in popularity.
3. Pg 124 Karl Schwarzschild revived the idea of the dark star after reviewing Einstein’s theories of relativity.
4. Pg 121 Einstein didn’t believe that black holes existed so the thinking of black holes didn’t come directly from his writing or thoughts.
5. Pg 122 “When a corpuscle of light is launched from such a star (black hole) with the standard light velocity, it will fly upwards at first, then slow to a halt and fall back to the star’s surface”.
6. Pg 131 Light is redshifted basically to infinity trying to leave a black hole.
7. Pg 134 The speed of light is constant trying to leave the black hole.

B. I’m interested in the really fundamental thinking that goes into scientists belief that black hole’s can exist. We know that Einstein did not support the idea of black holes while modern scientists do. So black holes were not explicitly written into General Relativity by Einstein. It appears that the whole basis of whether black holes can exist is based on whether light (boson) is affected by gravitationally warped space-time in exactly the same way as matter (fermion). On Pg 124 of “Black Holes and Time Warps” Kip Thorne fast forwards to a conclusion that General Relativity supports black holes but doesn’t go through the analysis of why. It appears that the whole basis of whether black holes can exist is based on whether a boson is more like a ballistic particle similar to a cannonball as opposed to a thing crawling in relation to a background entity. So here are some questions for discussion.

1. Did Einstein assume that light was a type of ballistic particle in his General Relativity theory? I know Einstein did not agree with what is called the ballistic theory of light, but this is the best terminology I can think of. I know he did not believe in a particle based ether that light waves traveled in relation to either. But did he clearly imagine that light would gradually slow down traveling in gravitationally warped space-time in exactly the same way as if a matter particle had been thrown upwards at light speed?
2. Einstein even said that light travels at constant speed while matter does not so didn’t he just say that bosons and fermions didn’t behave in exactly the same way in relation to space-time?
3. Did Einstein ever imagine that light was in some way crawling in relation to space-time rather than a just a ballistic particle? Is there anything in General Relativity that suggests either model?
4. How did modern scientists such as Schwarzschild come to the conclusion that light was basically a ballistic particle? Was it more or less an assumed thinking based on light being a particle or did they spend a lot of time arriving at exactly what kind of thing light was and how it behaved? I can’t really find a reference that suggests Einstein spelled out exactly what light was so scientists couldn’t have simply borrowed Einstein’s ideas on the topic. I know John Michell based his thinking on the Newton corpuscle model of light being affected by gravity.
5. Does Quantum Mechanics and the Standard Model also suggest strongly that light behaves primarily like a ballistic particle in very strong gravitationally warped space-time?

 

[RandallB]

5. Does Quantum Mechanics and the Standard Model also suggest strongly that light behaves primarily like a ballistic particle in very strong gravitationally warped space-time?

NO
This is where SR-GR and QM-SM are two different and incompatible theories. Which is why it is such a hard task for many that try unifying them somehow – something big has to change and what to change (IE which is wrong) is a tough and controversial choice to make or try. Both are very well like theories.
But one assumes gravity is based warped space-time requiring no “Particle exchanges” while the other accounts for gravity only by exchanges of Force Particle exchanges (gravitons and Higgs particles/fields not yet found).

Also, I don’t think “ballistic” needed to be defined or assumed for Schwarzschild to apply GR and the math to explain how he thought light would behave to establish the possibility of what we now call a Black Hole.
And sure at the time with the math saying it could and might is one thing,
then - opinions divided on whether or not nature should or would fill that possibility,
now - we are pretty sure it can and does, thus confirming some opinions, others not so much.

 

[Jonathan Scott]

Electromagnetic waves (including light) travel at the same speed relative to any observer. For purposes of relativity, light was originally assumed to consist of waves, but it doesn't matter if is it now alternatively treated as a collection of massless particles, as the result is the same. A material object traveling at very nearly the speed of light follows the same path in a gravitational field as a light beam.

Black holes do not in any way require light to be treated as particles.

The existence of black holes is not necessarily implied by Einstein's General Theory of Relativity alone.

When Schwarzschild first came up with a spherically symmetrical exact solution of Einstein's field equations, he assumed a point mass at the center of his system, where r = 0. His solution did not include black holes or anything like that. He also pointed out that the solution could be described in simpler mathematical terms using a different radial coordinate R, which was not however 0 at the mass location, but rather 2GM.

Later Hilbert made Schwarzschild's solution known more widely, but he ignored Schwarzschild's original assumption and effectively assumed instead that the mass was located where the new "Schwarzschild" radial coordinate R was zero. This had no effect on the solution outside the original mass position (where r = 0 and R = 2GM), but gives weird results within that radius, leading to the theory of black holes. It appears that few people have questioned this assumption since, although Marcel Brillouin questioned it almost immediately, and more recently Leonard S Abrams and others have attempted to call attention to it. The conventional view of GR seems to be that Hilbert's assumption should not be questioned, which seems somewhat unscientific to say the least.

Unfortunately, some of the people attempting to call attention to Hilbert's assumption are behaving as if this undermines the whole of GR and claim to find fault with just about everything else in relativity. This effectively undermines their own position and means that anyone else (such as myself) who questions Hilbert's assumption is also in danger of being labelled a crackpot.

So far, I have not seen any form of "proof" either way as to whether Hilbert's assumption or Schwarzschild's assumption is better, but as Schwarzschild's assumption was physically more plausible, I'm inclined to agree with it. I'd like to ask some GR experts what evidence they have that Hilbert's assumption is correct, but I think that by now that question in itself raises so many red flags that it's impossible to get a rational answer.

 

[Boffin]

C. Black holes can exist whether light is a particle or wave?
1. Thanks Jonathan Scott and RandallB for your replies on this issue. Kip Thorne lead me to believe that scientists who believed in a wave model of light did not believe that black holes could exist because of the waving or crawling nature of light. I read an article today that suggests that those scientists did not believe in black holes simply because they did not think that light was affected by gravity. This puts your comments in perspective. Is that basically what you both implied?
2. I still would like to pursue my questions B1,2,3,4 from #1 post. In B2 I suggested that bosons and fermions do not behave in exactly the same way in relation to space-time. I assume that both John Michell, Pierre Laplace, and Karl Schwarzschild assumed that light and matter behaved in the same way in the presence of gravity when they wrote their formulas for critical circumference. How much evidence did they and do we have of this? I know both light and matter are affected by gravity, but how much thinking did these earlier scientists do on that issue? What were their thoughts? Was this topic extensively researched?
3. Jonathan Scott, are you saying that some scientists question the assumptions used in the critical circumference formulae? Are some saying that if other valid assumptions are used then there would be no critical circumference? Seeing as Einstein didn’t believe that black holes exist, their existence is not written into GR. So the whole basis of whether black holes exist appears to be based on such critical circumference calculations? Is this correct?

 

[Jonathan Scott]

C. Black holes can exist whether light is a particle or wave?
1. Thanks Jonathan Scott and RandallB for your replies on this issue. Kip Thorne lead me to believe that scientists who believed in a wave model of light did not believe that black holes could exist because of the waving or crawling nature of light. I read an article today that suggests that those scientists did not believe in black holes simply because they did not think that light was affected by gravity. This puts your comments in perspective. Is that basically what you both implied?
2. I still would like to pursue my questions B1,2,3,4 from #1 post. In B2 I suggested that bosons and fermions do not behave in exactly the same way in relation to space-time. I assume that both John Michell, Pierre Laplace, and Karl Schwarzschild assumed that light and matter behaved in the same way in the presence of gravity when they wrote their formulas for critical circumference. How much evidence did they and do we have of this? I know both light and matter are affected by gravity, but how much thinking did these earlier scientists do on that issue? What were their thoughts? Was this topic extensively researched?
3. Jonathan Scott, are you saying that some scientists question the assumptions used in the critical circumference formulae? Are some saying that if other valid assumptions are used then there would be no critical circumference? Seeing as Einstein didn’t believe that black holes exist, their existence is not written into GR. So the whole basis of whether black holes exist appears to be based on such critical circumference calculations? Is this correct?

C. Yes.

1. I'd agree with that.

2. I don't know of any difference between how bosons and fermions would be affected by gravity. I don't know what Michell and Laplace assumed about light, but from the informal descriptions of what they said I'd guess they thought light and matter both followed Newtonian gravity. Schwarzschild would have known that things with the similar velocity are affected in the same way by space and time, so light would behave very similarly to a very fast particle.

3. As far as I know, the question about black holes comes down to the question "Where is the point-like mass in the vacuum solution". Schwarzschild assumed it was at his original r=0, which in Hilbert's "Schwarzschild coordinates" is where R=2GM/c^2. This meant that if the mass was actually of finite density, it was impossible to reach that radius, so the coordinate singularity where the metric factor (1-2GM/Rc^2) becomes zero cannot be reached. Hilbert assumed it was at R=0, which is "behind" the origin in Schwarzschild's original model. This means that if the mass becomes sufficiently dense in Hilbert's model, it can contract inside R=2GM/c^2 (which is then called the "event horizon") allowing various weird things to happen, as in black hole theory. I think that the vast majority of GR experts support Hilbert's assumption, but I suspect most of them don't even recognize that it's an assumption, and I've not found anyone prepared to justify it. That doesn't mean it's wrong, but it seems a lot less plausible than Schwarzschild's assumption. Note that apart from the question as to whether the mass can contract inside R=2GM/c^2 (and hence whether a black hole can form), the physics of the rest of the solution outside that radial coordinate is unaffected.

 

[Naty1]

Gravitational collapse is discussed in chapter 16, Pg 131 to 135, THE RIDDLE OF GRAVITATION, 1992, by Peter Bergmann a former student of Einsteins.

Here are a few excerpts

In 1939 Einstein published a paper in which he attempted to show that matter could not be so condensed that the Schwarchild radius would fall outside a gravitating body and thus become a reality. In the same year Robert J Oppenheimer ...(proved the opposite). The issues of stability, progressive condensation and collapse of very large masses are still with us today.

Bergmann also says

Oppenheimer and his collaborators postulated...various equations of state (for condensed matter) ...Einsteins approach was different...He did not trust (any assumption about equation of state)...because relativistic assumptions ...at very close range and high energies...might give rise to new phenomena which could invalidate theoretical results...he built up a concentration of mass from particles using atomic models sure to satisfy relativity no matter how unrelaistic or artificial in other respects...Einstein built up mass concentrations layer by layer...with atoms exerting no pressure radially...but considerable pressure at right angles to the radius

He goes to say theorists still disagree.

 

[Jonathan Scott]

Gravitational collapse is discussed in chapter 16, Pg 131 to 135, THE RIDDLE OF GRAVITATION, 1992, by Peter Bergmann a former student of Einsteins.
...
He goes to say theorists still disagree.

As far as I know, it appears that almost everyone at the time (including Hilbert) had failed to notice that Hilbert's assumption about the radial coordinate was merely an assumption. The arguments were therefore mainly about whether it appeared to be physically possible for matter to be squeezed down densely enough to get inside its own Schwarzschild radius.

There is a paper by Marcel Brillouin about the location of the mass point (which has recently been stored in an English translation on the ArXiv) which shows that at least one person was aware of this assumption, but no-one seemed to notice.

 

[Naty1]

In Parallel Worlds, Michio Kaku says

General Relativity is like a rojan horse...lurkinmg inside are all sorts of demons and goblins including blacvk holes, white, holes, wormholesd, and even time machines, which defy common sense. Einstein himself thought they would never be found in nature..For years he fought strenously against these strange solutions...in 1922 mathematician Jaques asked Einstein what would happen if such a (black hole) singularit actually did exist. "IT WOULD BE A TRUE DISASTER FOR THE THEORY; and it would be very difficult to say a priori what could happen physcially because the formula does not apply anymore"...In 1935 Einstein and his student Nathan Rosen introduced wormholes into the world of Physics...in 1939 Einstein wrote a paper in which...he tried to dismiss dark stars, claiming they cannot be formed by natural processes...Einstein and Rosen had the novel idea of representing the electron as a black hole...the idea failed...

 

[spidey]

whether light is wave or particle,there is change in the velocity and path near massive bodies..so if such things like black holes exist,then light cannot escape..

Assumptions are justified if what the result of those assumptions are true..Einstein made assumption with velocity of light and relativity is proved by many experiments and hence the assumption should be valid..Now there are many candidates for black holes and many believe black holes exist and so the assumption Hilbert made should be correct..isn't it?

 

[Jonathan Scott]

whether light is wave or particle,there is change in the velocity and path near massive bodies..so if such things like black holes exist,then light cannot escape..

Assumptions are justified if what the result of those assumptions are true..Einstein made assumption with velocity of light and relativity is proved by many experiments and hence the assumption should be valid..Now there are many candidates for black holes and many believe black holes exist and so the assumption Hilbert made should be correct..isn't it?

Black hole candidates are mainly identified by whether they are so massive that they would be black holes if both GR and Hilbert's assumption are correct. As Hilbert's assumption doesn't affect the physics outside the surface of the object (or the event horizon if it's a black hole) the evidence as to whether it's really black is more difficult.

There is some evidence from differences in X-ray emissions for objects which are around the maximum mass for neutron stars that there may be some threshold effect suggesting a change of state, hence providing some support for black holes (although there are other possible explanations, as Abhas Mitra is keen to point out). On the other hand, there is also evidence suggesting that some super-massive black hole candidates have strong intrinsic magnetic fields, which if true would mean that they definitely could not be black holes (by the "no hair" theorem).

 

[spidey]

Black hole candidates are mainly identified by whether they are so massive that they would be black holes if both GR and Hilbert's assumption are correct. As Hilbert's assumption doesn't affect the physics outside the surface of the object (or the event horizon if it's a black hole) the evidence as to whether it's really black is more difficult.

There is some evidence from differences in X-ray emissions for objects which are around the maximum mass for neutron stars that there may be some threshold effect suggesting a change of state, hence providing some support for black holes (although there are other possible explanations, as Abhas Mitra is keen to point out). On the other hand, there is also evidence suggesting that some super-massive black hole candidates have strong intrinsic magnetic fields, which if true would mean that they definitely could not be black holes (by the "no hair" theorem).

Do u say if massive bodies have magnetic field then it cannot be black holes?
One of the type of black hole is rotating one.A rotating black hole should be having magnetic field. am i correct?

 

[Jonathan Scott]

Do u say if massive bodies have magnetic field then it cannot be black holes?
One of the type of black hole is rotating one.A rotating black hole should be having magnetic field. am i correct?

According to the "no hair" theorem, a black hole's fundamental properties only include mass, angular momentum and electric charge. If it is rotating, it can only have a magnetic field due to that overall charge, which is negligible for any realistic amount of unbalanced charge. On the other hand, if it is full of ordinary matter, it can contain vast (balanced) numbers of both positive and negative charges and it can have a huge magnetic field because every iron atom and nucleon can contribute to the field.

 

[spidey]

According to the "no hair" theorem, a black hole's fundamental properties only include mass, angular momentum and electric charge. If it is rotating, it can only have a magnetic field due to that overall charge, which is negligible for any realistic amount of unbalanced charge. On the other hand, if it is full of ordinary matter, it can contain vast (balanced) numbers of both positive and negative charges and it can have a huge magnetic field because every iron atom and nucleon can contribute to the field.

You say magnetic field come because of charge.Can magnetic field arise because of angular momentum?
I have a confusion with planet's magnetic field. is planet have magnetic field because of angular momentum and hence electric current in its core? Or is planet have electric current in its core and hence magnetic field?
i.e. from angular momentum --> Magnetic field --> Electric current in core
Or
from Electric current in core --> Magnetic field

 

[Jonathan Scott]

You say magnetic field come because of charge.Can magnetic field arise because of angular momentum?
I have a confusion with planet's magnetic field. is planet have magnetic field because of angular momentum and hence electric current in its core? Or is planet have electric current in its core and hence magnetic field?
i.e. from angular momentum --> Magnetic field --> Electric current in core
Or
from Electric current in core --> Magnetic field

A magnetic field always requires electric charge, but that can consist of equal amounts of positive and negative charge, resulting in no overall electric charge. For example, a current flowing in a loop of wire creates a magnetic field. (Note for example that the neutron has a magnetic moment but no electric charge, but it is assumed to contain balanced charge distributions internally due to quarks).

A planet's magnetic field is thought to be due to the dynamo effect from electric currents flowing within a liquid metal core. See "Dynamo theory" in Wikipedia for more details.

In the case of a black hole, the "no hair" theorem says that the black hole can have electric charge, but it cannot hold both types of charge, so any magnetism can only be due to the rotation of that unbalanced charge. If a black hole had a significant amount of unbalanced charge, it would preferentially attract matter with the opposite charge and hence neutralize itself, so this mechanism could not create a significant magnetic field.

 

[Boffin]

C3. As far as I know, the question about black holes comes down to the question "Where is the point-like mass in the vacuum solution". I think that the vast majority of GR experts support Hilbert's assumption, but I suspect most of them don't even recognize that it's an assumption, and I've not found anyone prepared to justify it.

Are you saying that there is no good way of telling whether the formulaes used to calculate whether black holes exist use the right assumptions?

 

[Jonathan Scott]

Are you saying that there is no good way of telling whether the formulaes used to calculate whether black holes exist use the right assumptions?

At present, as far as I know, General Relativity itself doesn't set the boundary conditions, so in the absence of some new compelling theory which does, all we have for now is experiment.

Personally, I would have said that Schwarzschild's original assumption was physically very reasonable, and that the weirdness of Hilbert's assumption should count against it.

Some supporters of Schwarzschild's assumption claim to have proof relating to rotational effects (for example I believe Abhas Mitra claims something to the effect that angular momentum of the Kerr rotating black hole solution cannot vary correctly under rotations unless it is zero, making the mass itself zero). However, so far I've not fully understood these arguments and in at least some cases I'm fairly sure they don't actually prove anything, although they are quite plausible.

On the other side, some supporters of Hilbert's assumption point out that an event horizon has a finite area, where they assert that Schwarzschild's model would expect it to be a point. However, I don't have any problem with this; if rulers start shrinking down proportionally to distance from the origin, the limit of area that they measure is finite, and in Schwarzschild's model you can't actually reach the origin because a central mass with finite density would prevent you from doing so.

 

[JustinLevy]

As far as I know, it appears that almost everyone at the time (including Hilbert) had failed to notice that Hilbert's assumption about the radial coordinate was merely an assumption.

Because it is NOT an assumption. That is a valid solution to Einstein's equations. The only thing remaining is whether it is possible to physically reach such a situation. Einstein felt the answer should be no. And as Naty1 pointed out, there was still disagreement in 1922. A lot has been learned since 1922 however. Many many theorems regarding black holes have been proven that show in many situations, assuming Einstein's theory of gravity describes the gravitational evolution, that a singularity will occur in finite time for an infalling piece of matter.

So the question has become now: is the assumption that Einstein's theory of gravity describes the gravitational evolution correct?

On small distances, we know that something has to change (the information paradox), but this would only need to save us from singularities... there can still be black holes in the sense of event horizons.


If you want an argument of why you can't consider the mass to 'start' at r=2GM, the particles on the surface would have to have infinite proper acceleration to maintain their position. Such a situation will naturally evolve to having the 'surface' below the event horizon according to GR itself.

 

[Haelfix]

"But one assumes gravity is based warped space-time requiring no “Particle exchanges” while the other accounts for gravity only by exchanges of Force Particle exchanges (gravitons and Higgs particles/fields not yet found)."

Slow down for a minute. To begin with the Higgs is not a force carrier.

Secondly the particles in quantum mechanics are in no sense the same as billiard balls. They are really field like excitations, and are completely compatible with both special and general relativity. Sometimes you cannot localize them, or find a good coordinate system where two spacelike separated observers can agree on their definitions, but in so far as their domain of applicability is nice (eg a local, flat epsilon ball and on mass shell) then they are perfectly fine with GR.

The source of the confusion I think resides in the idea that you have localize mass down to an infinitesimal volume in order to have a particle concept. But this is already the same problem in classical electromagnetism, forget about GR or SR. If you squeeze charge down into an infinitesimal volume, you will get infinities popping up all over the place. The solution of the problem is now well understood, and involves renormalization and quantum *fields*. In the gravity case, its expected and can be shown to be roughly the same.

 

[Jonathan Scott]

Because it is NOT an assumption. That is a valid solution to Einstein's equations. The only thing remaining is whether it is possible to physically reach such a situation. Einstein felt the answer should be no. And as Naty1 pointed out, there was still disagreement in 1922. A lot has been learned since 1922 however. Many many theorems regarding black holes have been proven that show in many situations, assuming Einstein's theory of gravity describes the gravitational evolution, that a singularity will occur in finite time for an infalling piece of matter.

So the question has become now: is the assumption that Einstein's theory of gravity describes the gravitational evolution correct?

On small distances, we know that something has to change (the information paradox), but this would only need to save us from singularities... there can still be black holes in the sense of event horizons.

The arguments around 1922 were based on Hilbert's hidden assumption that the centre of the mass point is at r=0 rather than r=2GM (Schwarzschild's original mass point location), which was apparently noticed in a paper by Marcel Brillouin (available in translation as arXiv:physics/0002009). Einstein was hoping for a physical mechanism which would always prevent the central mass from being compressed into a radius smaller than 2GM, but did not find one.

I'm still trying to understand how the interior solution joins on to the exterior solution in the Hilbert interpretation, because Schwarzschild's own interior solution (available in translation as arXiv:physics/9912033) was, like his original vacuum solution (arXiv:physics/9905030), based on the assumption of the mass origin being at his original r=0 in polar coordinates, equivalent to R=2GM in the Schwarzschild vacuum radial coordinate. Since the boundary conditions for the interior solution are set by the way in which it joins to the exterior solution, Hilbert's assumption must mean that the physical solution has changed too (as should be obvious from the fact that it allows black holes).

The proof that a singularity will be reached in a finite time assumes the presence of an event horizon, which again only occurs with Hilbert's assumption.

If you want an argument of why you can't consider the mass to 'start' at r=2GM, the particles on the surface would have to have infinite proper acceleration to maintain their position. Such a situation will naturally evolve to having the 'surface' below the event horizon according to GR itself.

Sorry, but this argument is not at all valid, as I'm sure you'll see yourself if you think about it a bit more; if r=2GM is the origin so there is nothing "behind" it, then there is nowhere for mass to reside to create an event horizon at r=2GM.

 

[Boffin]

In 1939 Einstein published a paper in which he attempted to show that matter could not be so condensed that the Schwarchild radius would fall outside a gravitating body and thus become a reality. In the same year Robert J Oppenheimer ...(proved the opposite). The issues of stability, progressive condensation and collapse of very large masses are still with us today.

As far as I know, the question about black holes comes down to the question "Where is the point-like mass in the vacuum solution". Schwarzschild assumed it was at his original r=0, which in Hilbert's "Schwarzschild coordinates" is where R=2GM/c^2. This meant that if the mass was actually of finite density, it was impossible to reach that radius, so the coordinate singularity where the metric factor (1-2GM/Rc^2) becomes zero cannot be reached. Hilbert assumed it was at R=0, which is "behind" the origin in Schwarzschild's original model. This means that if the mass becomes sufficiently dense in Hilbert's model, it can contract inside R=2GM/c^2 (which is then called the "event horizon") allowing various weird things to happen, as in black hole theory.

D. Real basis of the black hole formulas?
1. Messages from Naty1 and Jonathan seem to indicate that how much a massive body can be compressed is the central issue in whether black holes can exist? Do I understand the comments correctly?
2. "Black Holes and Time Warps" pg 136 Kip Thorne mentions that Einstein did not believe that massive bodies could ever be compressed so much that they would form black holes.
3. We assume that the issue of whether black holes can exist is based on how small massive bodies can be compressed? Or can we understand this issue a different way?
4. We typically see the Hilbert and Schwarzschild formulas. But I personally haven't seen how they were developed, what assumptions were used, which more basic formulas were combined.
5. Jesse Kirkham in his website article "Black Holes - Relativistic escape velocity" actually develops the formulas which show that black holes can not even exist if the body were to be compressed infinitely small. For this formula, as the mass of the gravitational body approaches infinity, and/or an objects proximity to the body approaches zero, the escape velocity approaches c, the speed of light. But because photons leave the surface traveling at the speed of light, their speed will always be slightly higher than the escape velocity. Therefore black holes cannot exist.
6. Jesse Kirkham's other conservation of energy thought experiment proof makes equal sense to me. So are his formulas correct? They aren't rocket science but are based on very basic relativistic formulas.
7. So why do the formulas for Hilbert and Schwarzschild come up with different conclusions? Why did Einstein conclude that if a massive object was compressed enough it could form a black hole. Were they all not using these basic relativistic formulas that Jesse Kirkham has developed?

 

[Jonathan Scott]

D. Real basis of the black hole formulas?
1. Messages from Naty1 and Jonathan seem to indicate that how much a massive body can be compressed is the central issue in whether black holes can exist? Do I understand the comments correctly?

That was the issue that Einstein and others were considering. It is not the same as the issue of whether Hilbert's assumption or Schwarzschild's assumption was correct, which as I've already stated is a matter of where the mass point is assumed to be physically located.

I've had a quick look at Jesse Kirkham's stuff and it is irrelevant; it attempts to describe black holes using only Special Relativity, which is somewhat pointless.

 

[Boffin]

I've had a quick look at Jesse Kirkham's stuff and it is irrelevant; it attempts to describe black holes using only Special Relativity, which is somewhat pointless.

Are you saying that black holes can't exist acccording special relativity or are you saying something else? Are Jesse Kirkham's formulas and interpretation accurate according to special relativity?

 

[JustinLevy]

The arguments around 1922 were based on Hilbert's hidden assumption that the centre of the mass point is at r=0 rather than r=2GM (Schwarzschild's original mass point location)

That makes absolutely no sense. The center of mass is at r=0 in both solutions. Schwarzschild did not say the center of mass point is at r=2GM. You are seriously mis-interpretting things to try to fit your strange view.

You seem to be claiming these two separate things are historical disagreements of viewpoints:
1) whether mass can collapse to a singularity in GR
2) whether in a spherically symmetric situation, a pointlike singularity due to mass at the origin should be at r=0 or r=2GM


#1 was indeed a historical dicussion, it has now been proven in many general situations that a singularity evolves in GR

#2 however was not a historical disagreement of viewpoints. This is only something you have made up.

based on the assumption of the mass origin being at his original r=0 in polar coordinates, equivalent to R=2GM in the Schwarzschild vacuum radial coordinate.

No. If R=2GM was the origin, then the origin is not a point, but a finite sized sphere. At R=2GM, the circumference is non-zero.

The apparent bizarreness at the event-horizon is just due to the choice of coordinates. If you use a more appropriate coordinate system you can explicitly see that nothing strange happens according to a freefalling observer passing the event-horizon.

The ONLY difference in historical viewpoints was whether or not mass could collapse beyond this R=2GM. That is it. There is no other "assumption" like you keep claiming.

Sorry, but this argument is not at all valid, as I'm sure you'll see yourself if you think about it a bit more; if r=2GM is the origin so there is nothing "behind" it, then there is nowhere for mass to reside to create an event horizon at r=2GM.

Again. Schwarzschild never claimed R=2GM was the origin.

The Schwarzschild solution is a valid vacuum solution outside a spherical static mass. Do you disagree with this?

Okay, now imagine using it for a non-rotating star. The radius of the star is > 2GM. Where is the center of mass using schwarzschild's coordinates? The answer is R=0.

Let the radius of the star decreas some. Where is the center of mass now? Still R=0.

Let it collapse just till R=2GM. Are you saying suddenly all that spacetime inside the star ceases to exist from this time onwards, and R=2GM is just a point which is the center of mass?

This effectively undermines their own position and means that anyone else (such as myself) who questions Hilbert's assumption is also in danger of being labelled a crackpot.

The reason it is in danger of being labelled a crackpot is because you are seriously misunderstanding something basic here, and arguing against not Hilbert's math but some self-imposed belief of what Schwarzschild and Hilbert said which is not true.