What Happens to Neutron Stars Without Black Holes?

[land_of_ice]

If black holes are not real, just wondering? By the way they may or may not exist. But since some people don't believe they exist and some do, then if you DO NOT , how do you explain what happens to neutron stars that are 20 -25 the size of the sun?

typo in the title, it should read: " what happens to black holes" the typo is where it says "we", how that got there is not clear but , anyways.

 

[ansgar]

the evidence for BH are clear, one should believe in them.

 

[Cyosis]

There are no neutron stars that are 20-25 times the size of the sun.

 

[Phrak]

the evidence for BH are clear, one should believe in them.

Please, do tell. 1) What evidence distinguishes a black hole from collapsing matter that will become a black hole in infinite time where we may either measure time as cosmological time or the time on the clocks of us observerse here on Earth? I'm getting very upset with those who evidently pick up their physics leasons from the producers of the science channel without further ado. 2) What electromagnetic evidence or otherwise can distinguish a massive object, where the bulk of the matter occupies a thin layer on the causual side of critical radius, per the overlayed Minkowskian coordinate system of the Earthly observer, from a black hole?

 

[ansgar]

Please, do tell. 1) What evidence distinguishes a black hole from collapsing matter that will become a black hole in infinite time where we may either measure time as cosmological time or the time on the clocks of us observerse here on Earth? I'm getting very upset with those who evidently pick up their physics leasons from the producers of the science channel without further ado. 2) What electromagnetic evidence or otherwise can distinguish a massive object, where the bulk of the matter occupies a thin layer on the causual side of critical radius, per the overlayed Minkowskian coordinate system of the Earthly observer, from a black hole?

pick up any astrophysics textbook dude

 

[russ_watters]

Please, do tell. 1) What evidence distinguishes a black hole from...

Nothing worth nitpicking a definition over.

We've had the discussion before: that black holes exist is not in doubt. What their exact nature is is still being researched...kinda like with every other phenomena in science.

 

[Count Iblis]

Please, do tell. 1) What evidence distinguishes a black hole from collapsing matter that will become a black hole in infinite time where we may either measure time as cosmological time or the time on the clocks of us observerse here on Earth? I'm getting very upset with those who evidently pick up their physics leasons from the producers of the science channel without further ado. 2) What electromagnetic evidence or otherwise can distinguish a massive object, where the bulk of the matter occupies a thin layer on the causual side of critical radius, per the overlayed Minkowskian coordinate system of the Earthly observer, from a black hole?

You can investigate this using well defined alternative model. See e.g. http://arxiv.org/abs/gr-qc/0609024" .

 

[Jonathan Scott]

I think it is quite likely that black holes arise only as the result of a plausible but incorrect mathematical assumption on the part of Hilbert, who modified Schwarzschild's original assumption about the boundary conditions on the radial coordinate. That is, Einstein's field equations are correct but the assumption that the Schwarzschild radial coordinate can actually pass r = 2Gm/c² is physically incorrect, as this is the location of the (admittedly extremely hypothetical and unphysical) "point mass" in Schwarzschild's original solution.

A paper supporting this point of view was written by Marcel Brillouin in 1923, and this idea was resurrected by Leonard S Abrams and by Salvatore Antoci and others recently (including Stephen J Crothers, who has an unfortunate tendency to overstate the case and find fault in everything else as well). You can easily find them on Google if you are interested. English translations of some of the key historical papers have been made available on the ArXiv to help clarify the situation.

However, for reasons which puzzle me greatly, this is a topic which supporters of standard GR (as reformulated by Hilbert) consider heretical - a most unscientific concept - and most arguments on the subject seem to consist of being rude about the opposition. There may be a sound scientific argument for the standard GR position, and I would welcome such clarification, and I have for example seen papers claiming to refute these ideas specifically, including one by Malcolm MacCallum at arXiv:gr-qc/0608033. However, in each case it appears to me that the argument has missed a key point and has in some way implicitly assumed a result which depends on the point it is trying to prove. As far as I can see, GR does not specify the boundary conditions and hence it is possible that neither position can be proven, but Schwarzschild's original position seems more physically plausible, even though Hilbert's is more mathematically compelling.

If black holes do not occur for this reason, then extremely dense masses would still have exactly the same gravitational field outside their surface as predicted by standard GR at present, but the effective location of the center of the mass as mapped in terms of the exterior coordinate system would be at a point whose Schwarzschild radial coordinate effectively approaches the Schwarzschild radius as the density increases towards infinity. (This model works anyway, as can be confirmed by imagining the mass as being a thin hollow sphere and poking a radial ruler in through a hole). Note also that as the mass would still be made of normal matter, it could have an huge intrinsic magnetic field, and there is some evidence supporting the idea that some quasars have such intrinsic fields (although there are also theories of how a classical black hole could have the "frozen" remains of such a field anyway).

I also suspect that GR may not be totally accurate anyway in many cases, such as on the galactic and cosmological scale, and indeed down at the quantum scale, but from the experimental evidence it does seem extremely accurate for the simple case of a spherically symmetrical static central mass, as in this case, even if this has not yet been proven to be totally accurate for very strong fields. There is of course also the possibility that Einstein's Field Equations are not quite right in this case anyway. However, even if they are exactly right (at least locally), I'm still not convinced that they lead to black holes, although I hope I'm still open to being convinced if the right evidence comes along.

 

[Phrak]

Nothing worth nitpicking a definition over.

We've had the discussion before: that black holes exist is not in doubt.

Please provide a reference to substantiate this claim. The arguments I have been presented, in this forum, have not been well informed. Using the word 'exist', without qualification lends further doubt; we are comparing time intervals, one to another, where the relation between the two is not well behaved. 'Existence' should be used in a relative way, if at all.

 

[Patrus89]

Please provide a reference to substantiate this claim. The arguments I have been presented, in this forum, have not been well informed. Using the word 'exist', without qualification lends further doubt; we are comparing time intervals, one to another, where the relation between the two is not well behaved. 'Existence' should be used in a relative way, if at all.

I registered specifically for this thread. Would I be correct in assuming that you believe a black hole never finishes collapsing? I can see how you would view a singularity in this fashion, but to me a black hole is defined by its massive nature and event horizon. Do you believe that these massive bodies could theoretically be directly observed and would not be within an event horizon? I don't understand how that squares with observations of galactic nuclei, or even stellar mass black holes.

I don't believe that many people believe that there is a point of infinite density and zero volume at the heart of a black hole, but that doesn't mean they are behind an event horizon, making that speculation academic and semantic in the absence of quantum gravity.

 

[russ_watters]

Please provide a reference to substantiate this claim.

Your request is not applicable. There isn't anything to substantiate any more than there is to prove your name is "Phrak". And besides which, we've already had plenty of discussions on the issue of how well black holes are understood (which is a completely separate issue from whether they exist). There is no need to rehash. The problem, as before, is that you're mixing theory with observation. A "black hole" is a colloquial name given to an observed object (like "Phrak"). The name itself includes no claims about the exact nature of that object. A theory exists to describe the object, but whether the theory is correct or not has no bearing on whether the object exists. It exists.

Consider the phenomena called "Venus". Does it exist? What about when the ancients viewed it and gave it the name "Venus"? They "theorized" about what it was and were waaaaay off, but today we recognize that they were looking at the same "Venus" we are, they just didn't understand what it was.

Now with black holes, I suspect of we ranked the properties that define a "black hole" by importance and certainty, we'd probably end up 90+% certain that we understand what a "black hole" is. But even if we ended up being 99% wrong, that's only wrong in the understanding, not in the fact that the object we are trying to understand exists.

Using the word 'exist', without qualification lends further doubt...

The word "exist" can only be used without qualification. It's definition requires it. It is completely binary: something either exists or it doesn't.

 

[JustinLevy]

I think it is quite likely that black holes arise only as the result of a plausible but incorrect mathematical assumption on the part of Hilbert
...

However, for reasons which puzzle me greatly, this is a topic which supporters of standard GR (as reformulated by Hilbert) consider heretical - a most unscientific concept - and most arguments on the subject seem to consist of being rude about the opposition. There may be a sound scientific argument for the standard GR position, and I would welcome such clarification

You keep bringing this up. I am willing to try to help, but as many people have tried before, it is hard to understand what you are not accepting. Please answer these questions to help build a foundation of what is agreed upon personally, and where you personally start to disagree.

1) True/False? General relativity is a deterministic theory. Given appropriate initial conditions, there is only ONE solution.

2) Einstein proved that in GR a mass, beyond a certain radius, cannot support itself (ie. no static solution is possible). And furthermore Penrose proved that generically a singularity must form.

3) Hilbert's solution is a valid solution to the GR equations, if one considers a line singlarity/boundary of spacetime in the center of the event horizon (and this singularity is of zero volume in spacetime). Your suggested solution is a valid static solution only if one considers spacetime to have a boundary (not just a singularity) at the Schwarzschild radius (and this boundary in spacetime is cylindrical with finite area).

4) Consider a collapsing star. Take a spatial slice of spacetime, and initially there is no singularity. In the simplest cases (full spherical symmetry, dust solution, etc), the unique end solution is what you call "Hilbert's" solution.

5) Are you claiming, in more general collapsing cases, a non-zero area boundary of spacetime instantly appears? Or are you saying a zero-area boundary (point) shows up in a slice of spacetime, then grows to the Schwarzschild radius? What dynamical equations are you using to claim the movement/growth of a spacetime boundary?


This is only a guess, but I think the problem you are having is due to the fact that the usual spherical black hole solution is often (and was historically) derived as a vacuum solution, with the "source" term actually just handled as a boundary condition or interpreting the integration constants in some Newtonian limit. This seems to be leading you to thinking the "source" is a merely a mathematical choice we can argue about. When in reality, GR is a deterministic theory, and while difficult to solve analytically, now-a-days we can solve numerically. Starting from a star and letting it collapse does not yield the cylindrical boundary in spacetime you are claiming. These are not solved as vacuum solutions, as the matter source are considered directly. There is no mathematical "choice" to the solution here. Does this realization help? If not, can you explain better your personal disagreements with these calculations (please don't link me a paper and have me try to guess your understanding)?

 

[atyy]

"a configuration that is a black hole for (almost) all practical purposes, but might be missing the one key ingredient of having a horizon."
http://arxiv.org/abs/0902.0346

"If the central object is not a black hole, but rather a boson star or something similar, then the inspiraling object will continue to emit long after it would shut off in Kerr (Kesden et al. 2005). This would be a clean and blindingly simple falsification of the central black hole paradigm."
http://arxiv.org/abs/0903.0100

 

[Jonathan Scott]

You keep bringing this up. I am willing to try to help, but as many people have tried before, it is hard to understand what you are not accepting. Please answer these questions to help build a foundation of what is agreed upon personally, and where you personally start to disagree.

1) True/False? General relativity is a deterministic theory. Given appropriate initial conditions, there is only ONE solution.

2) Einstein proved that in GR a mass, beyond a certain radius, cannot support itself (ie. no static solution is possible). And furthermore Penrose proved that generically a singularity must form.

3) Hilbert's solution is a valid solution to the GR equations, if one considers a line singlarity/boundary of spacetime in the center of the event horizon (and this singularity is of zero volume in spacetime). Your suggested solution is a valid static solution only if one considers spacetime to have a boundary (not just a singularity) at the Schwarzschild radius (and this boundary in spacetime is cylindrical with finite area).

4) Consider a collapsing star. Take a spatial slice of spacetime, and initially there is no singularity. In the simplest cases (full spherical symmetry, dust solution, etc), the unique end solution is what you call "Hilbert's" solution.

5) Are you claiming, in more general collapsing cases, a non-zero area boundary of spacetime instantly appears? Or are you saying a zero-area boundary (point) shows up in a slice of spacetime, then grows to the Schwarzschild radius? What dynamical equations are you using to claim the movement/growth of a spacetime boundary?


This is only a guess, but I think the problem you are having is due to the fact that the usual spherical black hole solution is often (and was historically) derived as a vacuum solution, with the "source" term actually just handled as a boundary condition or interpreting the integration constants in some Newtonian limit. This seems to be leading you to thinking the "source" is a merely a mathematical choice we can argue about. When in reality, GR is a deterministic theory, and while difficult to solve analytically, now-a-days we can solve numerically. Starting from a star and letting it collapse does not yield the cylindrical boundary in spacetime you are claiming. These are not solved as vacuum solutions, as the matter source are considered directly. There is no mathematical "choice" to the solution here. Does this realization help? If not, can you explain better your personal disagreements with these calculations (please don't link me a paper and have me try to guess your understanding)?

I'm not sure how far this can be taken in this forum, but I'll try to summarize how the alternative viewpoint can be understood in terms of standard theory.

Although the Schwarzschild external and internal radial coordinates share a common definition, they do not behave in the same way, and the rate of change of this coordinate with respect to proper radius has a discontinuity at the surface of the spherical object, so it is not at all like a physical radius, even with appropriate scale factor.

Schwarzschild originally assumed a hypothetical point mass at the origin of his solution, defining a conventional radial coordinate in terms of x, y and z. When his original coordinate system is converted to the simplified "Schwarzschild radial coordinate" r (as named by Hilbert), the origin of his original coordinate system corresponds to r=2Gm/c². If you use the alternative way of defining this coordinate in terms of proper areas of spheres and extend this to the interior, you find that this radial coordinate value refers to the outside surface of the point (which has finite area despite being a point) but the middle of the point has Schwarzschild radial coordinate 0. This doesn't make much sense, so instead of considering something which effectively involves a factor of 0/0, we need to think about limits.

If we assume the object is slightly larger than a point in Schwarzschild's original model (so its surface is at r > 2Gm/c²), we can see that the radial coordinate decreases through 2Gm/c² to 0 within the object, and we conclude that the middle of the object is located at r=0, which is therefore that much "further in" than the original, suggesting that Schwarzschild's original model need to be stretched to insert an inner sphere. Hilbert therefore changed the exterior solution model to assume that the origin of that model was at r=0, implying that there is some sort of physical space between r=0 and r=2Gm/c² which could in theory appear in the exterior solution. Mathematically this also seems more general, because there is a singularity at r=0 but only a coordinate singularity at r=2Gm/c².

However, if you look at the scale of the radial coordinate just outside the surface of the object compared with proper radial displacement, and extrapolate that same scale into the middle of the object, you find that in terms of the external radial coordinate, the location of the middle approaches r=2Gm/c² as the mass shrinks. To avoid the complexities of internal solutions, you can simplify the model to a thin hollow rigid spherical shell whose external field is the same as that of the original mass. Inside that shell we have flat Minkowski space whose proper radius decreases towards the Schwarzschild radius as the external Schwarzschild radial coordinate shrinks towards the same value. Oddly, it seems that if the shell tries to collapse, the spatial coordinates shrink in such a way that its internal radius merely gets a little closer to 2Gm/c².

This means that Schwarzschild's original position that the physical origin of the exterior solution is the point where the exterior Schwarzschild coordinate r reaches 2Gm/c² seems to work perfectly well, and the interior solution, shrunk down very small relative to the exterior coordinate system, still fits between the outside and the inside of the mass without needing to move its origin.

In answer to your numbered questions:

1) Yes, I agree GR is deterministic (that seems obvious)

2) The proof that collapse is unavoidable depends on Hilbert's change of origin, which Einstein appears to have accepted (presumably because Hilbert was clearly the greater mathematician, even though the difference is physics rather than mathematics).

3) There is no boundary or discontinuity involved in space-time, although the Schwarzschild radial coordinate behaves abruptly in a different way once it reaches a surface.

4) The standard interior solution is defined by continuity with Hilbert's version of Schwarzschild's exterior solution, and that is what allows collapse.

5) There is no boundary or discontinuity. The explanation is given above.

 

[JustinLevy]

Hmm... #1 was a gimme, yet unfortunately that is the only one you agreed with.

You seem to be misunderstanding something involving the coordinates. So let me try to reformulate some of what I already said in a coordinate independent manner.

1a) Regardless if you choose to use a coordinate change r' = r + constant, the proper distances as defined by the metric are unchanged. Do you agree with this?

2) The proof that collapse is unavoidable depends on Hilbert's change of origin, which Einstein appears to have accepted (presumably because Hilbert was clearly the greater mathematician, even though the difference is physics rather than mathematics).

No, the proof does not depend on your choice of coordinates. Let's rewrite in non-coordinate terms to make this clear. Take a finite sized static spherically symmetric mass in GR. There is a non-zero "proper surface area" limit this object can have. This size limit is LARGER than the "event horizon" size limit. So well before reaching the "event horizon" size, the fate of such an object is sealed ... it must continue collapsing down to zero size.

So your comments on a static solution with the surface right at or above the event horizon limit are incorrect. Such a static solution in GR is not possible ... unless you artificially impose a boundary of spacetime of non-zero proper area. In which case the mass would run into this boundary in finite proper time (it still would not hover above the boundary).Regardless of confusion on coordinate choices for describing a black hole, I really really don't understand how you can wave away solutions that actually start with a non-rotating spherical mass and follow the collapse in. You already agreed the solution is deterministic. As I mentioned, the solution doesn't result in a singularity with a non-zero proper area. And the solutions are not coordinate system dependent (I hope we agree on that).

--------------
EDIT:
You continue to refer to the "Schwarzschild r=0" as a point. This is incorrect. Both mathematically, and physically. If you want to try to claim there is no spacetime existing in "Schwarzschild r<0", fine, and we can discuss that. But there can be NO debate that your "Schwarzschild r=0" is not a point in spacetime.

5) GR gives Ricci tensor = 0 in vacuum. This is a differential equation for the metric, and thus the solution will have integration constants. The difference between r' = r + constant choice in coordinates has its effect in the metric as a change in choice of the integration constants. To get the final solution we need to fix the integration constant by using the actual source terms (ie. consider the non-vacuum portion of spacetime) or appropriate boundary conditions.

Since, what you call "Hilbert's solution" is:
c^2 {d \tau}^{2} = <br /> \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \frac{dr^2}{\displaystyle{1-\frac{r_s}{r}}} - r^2 \left(d\theta^2 + \sin^2\theta \, d\varphi^2\right)
With the constant r_s = 2 G M / c^2. And by Birkhoff's theorem, this is the only solution outside a spherically symmetric mass. So the only thing we can do (and still have a valid GR solution in vacuum outside a spherically symmetric mass) is a change in coordinates.

Then with a change of variables \tilde{r} = r - r_s in order to have r=0 be on the event horizon, \tilde{r}=0 is NOT a point.

6) Schwarzschild started with x,y,z,t. The origin x=0,y=0,z=0,t=0 is a single point in spacetime. However he chose an integration constant which made r=0, theta=0 have a non-zero proper length from r=0, theta=pi. These are therefore clearly different spacetime points both mathematically (the two labels refer to distinct spacetime points) and physically (they are causally distinct).

So if you wish to use this coordinate system, you either need to impose a spacetime boundary at r=0, and admit r=0 is not a point. Or consider values r<0. You seem to instead be trying to choose r=0 is a point and there is no boundary ... this is wrong on multiple levels, and is not an available choice.

 

[Jonathan Scott]

I totally agree that Schwarzschild "point mass" solution is not realistic (and even less so than in Newtonian gravity), and that a point cannot meaningfully have a finite proper area.

However, Schwarzschild's "point mass" makes perfect sense as an idealized limit case of a mass of finite size being shrunk down towards a point without actually reaching it.

I also agree that mathematically, the exterior solution doesn't have a boundary at the Schwarzschild radius.

However, the exterior solution stops at the surface of the mass, and with Schwarzschild's original assumption combined with a not-quite-point mass, that surface remains outside the point as the mass shrinks. The extrapolated limit value of the exterior Schwarzschild radial coordinate at the middle of the mass (which can be formalized by poking a ruler calibrated in those units through the mass and assuming it to be hollow) tends to the Schwarzschild radius as the mass shrinks, suggesting that the middle can be considered to be physically located at a fixed point, at least as far as the exterior coordinate is concerned (which is of course the one used in the exterior solution).

There are of course other odd things that happen; as the mass shrinks down, it tends towards a limit proper size with a limit proper area. You'd think that for example if it were hollow you could lower the shell inward, but since that makes everything inside the shell shrink in approximately the same proportion, that doesn't work in the expected way. I don't claim to understand all the implications of this viewpoint, but I'll maintain that they are less weird than black holes.

I think the main source of confusion is the tendency to think of the Schwarzschild radial coordinate as being like a physical radius despite the well-known fact that it changes its nature very abruptly at the boundary between the exterior and interior solutions.

 

[Chronos]

The issue of whether a 'true' singularity can form in a collapse event may be debatable. Formation of an event horizon is not debatable.

 

[Dickfore]

Schwartzshild's solution is valid for any spherically symmetric distribution of matter in the region outside of that mass. It's similar to the fact that the gravitational field of a spherically symmetric mass outside the mass looks exactly like that of a point mass in Newton's gravity.

 

[JustinLevy]

However, Schwarzschild's "point mass" makes perfect sense as an idealized limit case of a mass of finite size being shrunk down towards a point without actually reaching it.

As already explained, there is no such asymptotic limit case. Before a mass collapses to the "event horizon size", it is already past the static limit. Beyond this, the spherical mass CANNOT prevent further collapse and will collapse to a point. Are you denying this?

Let's make this more clear:
1) Do you agree there is a non-zero surface area minimum size limit for a static spherical mass M?

2) Do you agree with Birkhoff's theorem, that the unique vacuum solution outside a spherical mass distribution is (written here in coordinate form):
http://en.wikipedia.org/wiki/Schwarzschild_metric
This is the only solution. If you want to write it in coordinate form, the only other solutions are mere coordinate transformations from this.

3) Do you agree if we look at the Schwarzschild metric in coordinate form for a freefalling observer, it takes a finite proper time to fall from the photon sphere (a location outside the event horizon) to the singularity?

4) Do you agree that a spherical mass collapsing beyond the minimum static limit size, the entire mass will collapse to a singularity in finite proper time? In other words, not only is there a minimum static size limit, but the mass can not "asymptotically approach" a different size (in effect giving a "pseudo"-static size)?

However, the exterior solution stops at the surface of the mass, and with Schwarzschild's original assumption combined with a not-quite-point mass, that surface remains outside the point as the mass shrinks.

Please stop bringing up the interior solution. The interior solution is moot to this discussion. The interior solution CANNOT prevent the collapse of the mass to a singularity beyond the static limit. The other question which you continue to avoid is:

Since you already agreed GR is deterministic, and numerical simulations of star collapse show the result is what you call "Hilbert's" solution. Are you claiming the numerical simulations are wrong?

There are many people that don't believe a singularity will form in reality. But there can be NO DEBATE about the predictions of a mathematical theory. GR is self-consistent. It predicts a collapsing star, if going beyond the static limit, will collapse beyond an event horizon.

If your intuition conflicts strongly with a black hole, or a singularity: fine. You are in good company historically, and even in current time on the later point. But please take the time to understand that there can be no debate about what General Relativity says about them in this very simplified and well understood context of a spherical mass collapsing.

I think the main source of confusion is the tendency to think of the Schwarzschild radial coordinate as being like a physical radius despite the well-known fact that it changes its nature very abruptly at the boundary between the exterior and interior solutions.

This again is focusing on moot aspects of the interior solution. Call that r whatever you want. In coordinate system independent terms, the proper area of the spherical mass will collapse to zero.

What you are bringing up is unrelated enough that I'm getting confused. Maybe I'm horribly misunderstanding your point and we are talking past each other.

5] Are you claiming that:

• A) a spherical mass collapsing, can never form an event horizon?

OR

• B) a spherical mass collapsing beyond the static limit will not go to a singularity in finite proper time, but asymptotically approach a finite proper area size (below the event horizon)?

OR

• C) a spherical mass collapsing beyond the static limit will go to a zero size proper area point, but (in some unclear sense) the "actual" radius will be non-zero?

OR

• D) Something else entirely?

EDIT:
While searching around for the simplest gravitational collapse model I could find, I got this from wikipedia:
Robert Oppenheimer and Hartland Snyder considered a model of a dust cloud, where the dust particles of the cloud were moving radially, towards a single point, and showed that the dust particles could reach the singularity in finite proper time. After passing the limit, Oppenheimer and Snyder noted that light cones were directed inwards, and that no signal could escape outside.
J.R. Oppenheimer, H. Snyder, "On Continued Gravitational Contraction", Physical Review 56 (1939) p455.

Can we at least agree in some cases gravitational collapse leads to an event horizon in GR? And that in this particular case, it leads to a zero surface area singularity?

 

[Phrak]

Those who have us believe there have been black holes observed located in galactic centers have a few things to explain.

1) What evidence distinguishes a black hole from an incipient black hole?

2) A 25 kilometer radius black hole takes forever to form in cosmological time. Explain how a 50 kilometer objects fits into a pre-inflation universe several order of magnitude smaller?

3) The casual, observable influence from an event horizon would require forever to reach us. Explain this one.

 

[Dmitry67]

Phrak, how do you define the word 'exists' (existed, will exist) in curved spacetime?

As there is no global 'NOW' in curved spacetime, I see no opton but to merge all 3 forms (exists now, existed, will exist) into 1 - exist(point in spacetime)
In this sense BH do exist of course

You can argue that some points are not reachable - for example, beyond cosmological horizon.
Then you can use a stronger form - exists and reachable (there is a lightcone going from you-now and hitting that point in sapcetime)
In this sense BH exist and are reachable too.

 

[Dmitry67]

But do we have any updates about objects more dense than neutron stars - quark stars and strangelet stars?

 

[Phrak]

Phrak, how do you define the word 'exists' (existed, will exist) in curved space-time?

As there is no global 'NOW' in curved space-time, I see no option but to merge all 3 forms (exists now, existed, will exist) into 1 - exist(point in spacetime)
In this sense BH do exist of course

I understand your point of view. Call these elements 'events' since that's what we call them anyway. We want to know if they are located somewhere on the spacetime manifold consisting of what is, was and will be--or not. We have to use a different language and say an event exists on the map when it may actually be in the causal future (will be) or in the causal past (was). We get around this language barrier as long as we speak the same mappish dialect and everything's fine until someone else misinterprets the dialect.

In this sense BH do exist of course.

I am not as certain as you. As best I can discern, some events, such as the formation of an event horizon are premised on a universe of infinite past cosmological time span. "Falling into a black hole" is premised upon an infinite cosmological future span. Are you prepared to argue either of these? Or am I mistaken on the requirements?

Thank you for helping me clarify the pertinent questions.

 

[Phrak]

The issue of whether a 'true' singularity can form in a collapse event may be debatable. Formation of an event horizon is not debatable.

Yet, here we are debating. Preferably we would not be debating, but discovering true things, where issues are not decided by the democracy of men, but the tyranny of nature.

 

[Dmitry67]

1. Well, if you define 'will' as 'in my casual future' (lightcone starting from you-now) the black holes do exist, because you can send a splash of light and it (will) hit the singularity.

You can also send a spaceship (now) and it will reach the singularity in finite (and very short) proper time

I don't understand what you mean by '"Falling into a black hole" is premised upon an infinite cosmological future span'. This is simply wrong. Falling into black hole is very short process.

 

[Dmitry67]

As best I can discern, some events, such as the formation of an event horizon are premised on a universe of infinite past cosmological time span.

Small correction: only the (abstract) notion of "absolute" horizon requires in fact knowledge of boundary conditions at infinite future (here you're right)

However, I am talking about the apparent horizon - which works as good approximation of absolute one for all practical purposes.

 

[Jonathan Scott]

As already explained, there is no such asymptotic limit case. Before a mass collapses to the "event horizon size", it is already past the static limit. Beyond this, the spherical mass CANNOT prevent further collapse and will collapse to a point. Are you denying this?

In Schwarzschild's original model, where the physical origin's location in terms of the exterior radial coordinate is effectively r=2Gm/c² (although to avoid the infinities this has to be taken as an extrapolated limit), this does not arise.

Let's make this more clear:
1) Do you agree there is a non-zero surface area minimum size limit for a static spherical mass M?

Yes.

2) Do you agree with Birkhoff's theorem, that the unique vacuum solution outside a spherical mass distribution is (written here in coordinate form):
http://en.wikipedia.org/wiki/Schwarzschild_metric
This is the only solution. If you want to write it in coordinate form, the only other solutions are mere coordinate transformations from this.

Yes.

3) Do you agree if we look at the Schwarzschild metric in coordinate form for a freefalling observer, it takes a finite proper time to fall from the photon sphere (a location outside the event horizon) to the singularity?

That's not relevant if you hit the mass before you reach where the event horizon would have been.

4) Do you agree that a spherical mass collapsing beyond the minimum static limit size, the entire mass will collapse to a singularity in finite proper time? In other words, not only is there a minimum static size limit, but the mass can not "asymptotically approach" a different size (in effect giving a "pseudo"-static size)?

In Schwarzschild's original model there is no minimum limit. However much the mass is shrunk, its proper radius tends to a limit of 2Gm/c² and in terms of the extrapolated exterior coordinate it is shrunk so much that its middle converges on the point where that coordinate would reach 2Gm/c².

All of this is about just one thing - a constant of integration in Schwarzschild's solution, which Schwarzschild explicitly assumed to be one thing, indicating that the mass is physically located at one point, and Hilbert explicitly changed to a different value, saying in a footnote that this was more general and mathematically unique (which is of course true). Almost everyone since then (including Einstein) simply accepted Hilbert's word for it (and Karl Schwarzschild was dead). However, this change has physical consequences (in giving rise to black hole theory) and needs a physical justification.

People who are familiar with Hilbert's version obviously find it difficult to distinguish between what parts of GR derive from this additional assumption and what parts are based on Einstein's Field Equations. For example, with Schwarzschild's position, the fact that the "point" has finite area is not relevant, because a finite mass could not be compressed to a point and that area is merely a hypothetical limit.

I must stress that I'm not sure either way about this. I find Schwarzschild's assumption more plausible and comfortable than Hilbert's, and I don't find any obvious inconsistency in it now, although I'm still puzzled by some aspects, and it was quite tricky getting to understand it without being confused by what I'd previously learned about black holes. What I'd like to find is some real evidence (theoretical or experimental) either way, but what seems to happen in practice is that I just get circular arguments from those who support the standard GR theory based on Hilbert's assumption (or occasionally from those who don't).

 

[JustinLevy]

In Schwarzschild's original model, where the physical origin's location in terms of the exterior radial coordinate is effectively r=2Gm/c² (although to avoid the infinities this has to be taken as an extrapolated limit), this does not arise.

Again, keep in mind that what you are calling the spatial "origin" here is not a point in space. We have already covered that.

Secondly, merely doing a coordinate transformation does NOT change the physical results, as the predictions of GR are independent of the choice of coordinates. The only way you can change the situation is to artificially add in a boundary to spacetime at the event horizon.

And lastly, even if we put in this boundary infalling matter will STILL hit this boundary in finite time. So even in this contrived case, this following comment is wrong:

That's not relevant if you hit the mass before you reach where the event horizon would have been.

Trying to narrow down where the misunderstanding is occurring, I think this next comment is quite illuminating.

All of this is about just one thing - a constant of integration in Schwarzschild's solution, which Schwarzschild explicitly assumed to be one thing, indicating that the mass is physically located at one point, and Hilbert explicitly changed to a different value

Yes, regarding the integration constant statement. But the conclusions you draw from this are incorrect. You seem to be missing some very important points here.

#1) There is no freedom to choose this integration constant. This integration constant comes about from solving the vacuum equation outside the mass. Once you consider the source equations (ie. the non-vacuum region), this FIXES the integration constant. You are instead trying to argue we solve just the vacuum region and are completely free to choose the boundary values. You are incorrect here.

Do you understand this?
This is why I keep bringing up examples of starting with a non-collapsed star (so we don't have to deal with arguments over singularities), and then allow it to evolve according to GR and watch it collapse. The result is NOT what you claim. Because this explicitly fixes the boundary term to something physical, it makes it easier to see where your error is. You keep ignoring these explicit examples.#2) If you want to consider his choice in integration constant, (or equivalently here, his choice of coordinates) you need to use \infty &gt;r&gt;-2GM/c^2. Otherwise, even though he started with a continuous coordinate chart (x,y,z,t), he somehow ended up with the "origin" not referring to a single point in space.

I am having trouble disentangling what mistake Schwarzschild made versus what is actually just a misunderstanding in your interpretation of his solution. So to help this along, can you please answer the following (hopefully this will help me and others understand your point of view better):

Post here explicitly what you are calling Schwarzschild's solution, using his coordinate chart, and specifying the valid ranges for each coordinate variable.

People who are familiar with Hilbert's version obviously find it difficult to distinguish between what parts of GR derive from this additional assumption and what parts are based on Einstein's Field Equations. For example, with Schwarzschild's position, the fact that the "point" has finite area is not relevant, because a finite mass could not be compressed to a point and that area is merely a hypothetical limit.

I must stress that I'm not sure either way about this. I find Schwarzschild's assumption more plausible and comfortable than Hilbert's, and I don't find any obvious inconsistency in it now

There is no freedom for another "assumption" here. Again, what you feel is a freedom to set this integration constant, is actually completely fixed when considering the non-vacuum (ie. source term) parts. That is why I keep brining up the explicit examples of calculating a collapsing star.

For an analogy. Consider simple electrodynamics. In vacuum we have:
\nabla^2 V = 0
Outside a static spherical charge distribution, due to the spherical symmetry we get:
\frac{1}{r^2} \frac{\partial}{\partial r} (r^2 \frac{\partial}{\partial r} V(r)) = 0

We can solve this and find generally that
\frac{\partial}{\partial r} (r^2 \frac{\partial}{\partial r} V(r)) = 0
\frac{\partial}{\partial r} V(r) = C_1 / r^2
V(r) = -C_1 / r + C_2

Note we can make a coordinate transformation (scaling and/or translating r):
V(r&#039;) = a_1 / (r&#039; + a_0) + C_2

If we demand the boundary condition V -> 0 as r-> infinity, we get
V(r&#039;) = a_1 / (r&#039; + a_0)
This satisfies the equations outside the spherically symmetric charge distribution.

You seem to think we are free to choose a_0 and a_1 however we want, and this amount to a mere assumption. This is not the case. Considering the source equations, provides one constraint and in effect fixes one constant in terms of the other. The remaining constant arises merely due to coordinate choice ... in which case we NEED to consider r' < 0 if we choose a_0 > 0, to cover all space.

Once the total charge in the distribution is specified, there is NO freedom "to make another assumption". And just like in the GR situation, the internal solution is irrelevant here (merely the total "charge"/mass is needed to fix the "integration constant" / boundary term).
Does this simple E&M analogy help (hopefully)?

Birkhoff's theorem says there is a unique physical solution in the GR case we are considering. You already agreed to this, but paradoxically keep claiming there is another physical solution. I'm trying my best, but this makes it impossible to really understand your claims.

 

[Jonathan Scott]

Most of what you are saying is either simply true for GR in general or alternatively only applies to the Hilbert assumption, and I know it's difficult distinguishing between those.

For the integration constant, you need to look at Schwarzschild's original vacuum solution paper and see what Hilbert changed (including his footnote). Salvatore Antoci has published papers on exactly that subject, including English translations of the relevant parts of original papers, which are surprisingly straightforward. In particular, see: arXiv:physics/0310104v1

Obviously the distant case is determined by flatness at infinity, and that is not disputed. The difference in constants is equivalent to where the origin is physically assumed to be. It is true that IF you assume Hilbert's position that the origin is where the Schwarzschild r=0 then the location in vacuum where r=2Gm/c² is not physically a point. However, if you take Schwarzschild's original model and use a not-quite-point mass to avoid the infinities then the origin is not part of the vacuum solution and the problems do not arise.

 

[JustinLevy]

For the integration constant ...

We don't need to argue by authority here. This is simple enough we can solve ourselves.

Do you, or do you not, agree that the integration constants from the vacuum solution are uniquely fixed by:
1) the boundary condition at infinity
and
2) the source term
?

This is not rhetorical. Please answer this question.

ALL your confusion seems to stem from your misunderstanding that what you set the integration constants to, or choice of coordinate chart, amounts to an additional assumption. It does NOT. We can solve for what that constant is. One is not free to choose it. And of course the predictions of GR are independent of what coordinate chart you choose.Furthermore, something you continue to avoid:
Consider the initial condition of a star that we then allow to evolve according to GR and collapse.

You already agreed GR is deterministic. So you must understand that there is only ONE solution. There are no "integration constants" to hide behind here. Everything follows from the initial conditions. The final collapsed solution is not what you claim it is. This is the simpliest and most direct counter to your claim against the "blackhole solution". If you really want to learn, at least start here and realize there is a mistake in your understanding. Without this realization, we'll keep talking in circles as you jump between conflicting statements to suit the need. Please, please pause and consider a non-vacuum solution ... and how it will evolve. GR is deterministic, and the unique solution is not what you are claiming.

Lastly. You agreed with Birkhoff's theorem which says there is a unique physical solution in the GR case we are considering. This should immediately make you realize the curvature at the surface of a spherical mass is not debatable like you seem to believe. So please stop claiming there is another physical solution. You seem to have bought into a talking point that what you call "Schwarzschild's solution" and "Hilbert's solution" provide two valid and physically distinct solutions to GR. That is incorrect.

This all started because you stated you'd like to learn more and understand what is and isn't correct about these conflicting views on black holes. It has been explained multiple times. There are even direct examples of non-vacuum solutions following a star collapsing to a black hole. What will it take for you consider the possibility that the talking point you've bought into is wrong? At the very least please continue responding to the questions so we can progress forward. Feel free to ask me questions too if you feel that will help.

 

[Jonathan Scott]

We don't need to argue by authority here. This is simple enough we can solve ourselves.

Do you, or do you not, agree that the integration constants from the vacuum solution are uniquely fixed by:
1) the boundary condition at infinity
and
2) the source term
?

This is not rhetorical. Please answer this question.

In a sense, what is affected is a third term, the origin.

The published papers by Salvatore Antoci (available in copy on the ArXiv) specifically address this point. A translation of the Schwarzschild original paper can be found at arXiv:physics/9905030v1 and an excerpt of Hilbert's paper where he changed the assumption can be found in Antoci's later paper: arXiv:physics/0310104v1

The difference does not affect the results outside the Schwarzschild horizon but simply whether one can reach it or not.

Antoci is not saying that Hilbert's assumption is necessarily wrong, but rather that Hilbert made a different mathematical assumption from Schwarzschild that has different physical consequences, in particular making black holes possible, and that there doesn't seem to be any theoretical way at present to prove either assumption correct or incorrect, but Schwarzschild's original idea avoids the problems of black holes even if it's mathematically less general.

I have tried to understand the detail myself, in particular Schwarzschild's original paper and what his model implies.

In the various arguments I've seen, those supporting Schwarzschild's original assumption do not have any obvious faults as far as I could see, and I've followed those up by doing my own modelling (including my conceptual picture of replacing the point mass with a hollow sphere in the standard solution and poking a ruler through it) to look for inconsistencies, which so far I've not found, but this is obviously not a well-researched area and there could well be problems I've missed (which is what I'm hoping to expose through discussion).

I'm also obviously satisfied that Hilbert's version (as in standard GR) is self-consistent too.

However, it seems to be near-impossible for anyone who has "grown up" with Hilbert's version to see the alternative picture and provide any constructive criticism of it. The arguments they present usually seem to be circular, based on assuming some aspects of Hilbert's position. I've also seen some really quite nasty attacks of the form "if you don't understand why Hilbert was right to correct Schwarzschild, you must be stupid", but this doesn't help me understand anything.

Personally, I feel that if I'm expected to accept the weirdness of black hole theory, I need to understand why in a way which really convinces me, which I'm not getting, and given that there appears to be an alternative which is still consistent with Einstein's field equations, I want to know why I should choose one over the other. (I accept weirdness when there's strong enough evidence for it, as with Bell's inequality and entanglement, but I don't like just being expected to take someone's word for it).

 

[George Jones]

These ideas have been thoroughly discredited; see

https://www.physicsforums.com/showthread.php?t=141985&highlight=Abrams

http://arxiv.org/abs/gr-qc/0608033.

This line of thought is promoted by a small group of people that is largely ignored by the physics community. As, such it is clearly not mainstream, and the Physics Forums rules,

https://www.physicsforums.com/showthread.php?t=5374,

in part, say,

Overly Speculative Posts: One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion.

Note that in the last quoted sentence the word "or" is used, not "and."

This decision has been reached after discussion by several Mentors.

Although Physics Forums Mentors are under no obligation to defend mainstream physics (as such action could result in unending bickering), in this particular case, I would like to put forward the mainstream's case, but, because of work and family commitments, I won't be able to do this until about two to three weeks from now.

This didn't happen.

When I have enough time, I will open up this thread for a while, and anyone who has posted (or not) will be invited to participate.

I have yet to find the time, and my non-PF pressures are more extreme now than they were then, but I do not rule out the possibility of in the future opening a special thread to discuss this.

Until then, posts about this stuff will be treated in the way posts about non-mainstream stuff are usually treated.