Graphical example of BH formation by PAllen

[TrickyDicky]

Unlike the singularity theorems, Birkhoff's theorem makes no assumptions about 'reasonable matter states'. Nothing is assumed except the Einstein Field equations.

Well yes, that is true as long as you don't count as assumption an (rather unphysical) isotropic vacuum universe.

Come to think of it, maybe isotropic vacuum is a redundancy, is a vacuum that is not isotropic conceivable?

 

[my_wan]

I kind of like the way PAllen constructed the thought experiment to. The one thing that appears to be missing in many of these descriptions is from the perspective of a person entering the black hole. From this perspective the notion that there is an event horizon to cross dries up, like chasing a mirage. As you approach a super massive black your local metric of spacetime is distorted such that the event horizon will appear to shrink away from you. This is because locally the speed of light is always constant such that the notion of a local horizon cannot correspond to a point at which the speed of light is exceeded. That's what keeps you safe from tidal forces while entering a supermassive black hole.

If we mix PAllen's description with an apparently shrinking event horizon, and assume the internal structure is still present when entered, then once the event horizon shrinks enough, such that not enough mass remains within the event horizon to produce an event horizon, the black hole will effectively have evaporated from their perspective.

My question, if this holds, is: would the time dilation (relatively slowed time) of a crew entering be sufficient that when this time dilation is taken into account would enough time pass for the external observer for the black hole to have evaporated from that perspective also, such as from Hawking radiation? In fact a number of interesting questions can be formulated.

I liked this graphical example of black hole formation posted by PAllen in another thread and I want to discuss it.

It is not unusual that arguments defending existence of black hole go like that:
1. Assume that BH exists.

This assumption is not problematic with or without GR. Black holes were theoretical entities long before relativity. Basically the above assumption is the equivalent of:
1. Assume gravity is strong enough that photons cannot escape.

In Newtonian physics this was simply due to an assumed mass of the photon. GR only made the description more variable depending on the world line of the observer providing the description. Sonic black holes are another interesting phenomena used to model some of these effects.

 

[zonde]

There is no need for such complexity unless you reject pure math: Birkhoff's theorem. Assuming spherical symmetry, and any shell of matter just inside its SC radius, it is guaranteed that the true horizon is at the SC radius and the apparent horizon is inside it by some infinitesimal amount. If you don't want to accept this, you have no choice but to admit that you reject GR, because this is pure mathematical proof. Unlike the singularity theorems, Birkhoff's theorem makes no assumptions about 'reasonable matter states'. Nothing is assumed except the Einstein Field equations.

I am not sure but isn't it result of Birkhoff's theorem that interior of spherical massive shell is flat spacetime?
In that case Birkhoff's theorem does not allow symmetrically collapsing shell as it would have to have curved spacetime inside it. Isn't it so?

 

[PAllen]

I am not sure but isn't it result of Birkhoff's theorem that interior of spherical massive shell is flat spacetime?
In that case Birkhoff's theorem does not allow symmetrically collapsing shell as it would have to have curved spacetime inside it. Isn't it so?

No (Birkhoff's theorem says nothing at all about interior of a shell); and No (Birkhoff's theorem in no way prevents or even says anything about a collapsing spherical shell except for the metric outside the shell.

It would really help to study basic GR before attempting to refute the understandings of those author's who have studied it for decades.

 

[zonde]

I kind of like the way PAllen constructed the thought experiment to. The one thing that appears to be missing in many of these descriptions is from the perspective of a person entering the black hole. From this perspective the notion that there is an event horizon to cross dries up, like chasing a mirage. As you approach a super massive black your local metric of spacetime is distorted such that the event horizon will appear to shrink away from you. This is because locally the speed of light is always constant such that the notion of a local horizon cannot correspond to a point at which the speed of light is exceeded.

I think that the utility of examples with free falling observers dries up at the moment when you try to construct global coordinate system where some background stays more or less static, isotropic and homogenous.

That's what keeps you safe from tidal forces while entering a supermassive black hole.

Tidal forces are not exclusively associated with event horizon. Tidal forces are present in any field of gravity.

This assumption is not problematic with or without GR. Black holes were theoretical entities long before relativity. Basically the above assumption is the equivalent of:
1. Assume gravity is strong enough that photons cannot escape.

In Newtonian physics this was simply due to an assumed mass of the photon. GR only made the description more variable depending on the world line of the observer providing the description. Sonic black holes are another interesting phenomena used to model some of these effects.

This assumption is problematic if you are trying to construct an argument about possible formation of black hole.
Look up Begging the question fallacy.

 

[zonde]

No (Birkhoff's theorem says nothing at all about interior of a shell); and No (Birkhoff's theorem in no way prevents or even says anything about a collapsing spherical shell except for the metric outside the shell.

Birkhoff's theorem says that purely longitudinal gravity waves do not exist and so perfectly spherical gravity waves do not exist as well. Changes in gravitational potential inside perfectly spherically symmetric collapsing shell can propagate only as perfect spherically symmetric gravity waves that do not exist according to Birkhoff's theorem.

It would really help to study basic GR before attempting to refute the understandings of those author's who have studied it for decades.

Let's make it clear. I see no problem with Birkhoff's theorem (so far). But I see problem with interpretation about what it implies.

We don't have perfect spherical symmetry in nature. As we go down the scale there is the level where granularity appears.

 

[PAllen]

Birkhoff's theorem says that purely longitudinal gravity waves do not exist and so perfectly spherical gravity waves do not exist as well. Changes in gravitational potential inside perfectly spherically symmetric collapsing shell can propagate only as perfect spherically symmetric gravity waves that do not exist according to Birkhoff's theorem.

Not only Birkhoff's theorem, but the most general spherically symmetric GR solutions simply have the result that a collapsing or oscillating matter that is spherically symmetric does not radiate, so there is no contradiction at all.

Let's make it clear. I see no problem with Birkhoff's theorem (so far). But I see problem with interpretation about what it implies.

We don't have perfect spherical symmetry in nature. As we go down the scale there is the level where granularity appears.

Of course there is no perfect spherical symmetry, but as with much of physics, we use a simple case to get at certain fundamentals. In this case, that both apparent horizon and true horizon exist may exist when there is no singularity (yet), and no great mass density. These conclusions are trivially provable per my argument given spherical symmetry. Do you argue that a slight deviation from such symmetry radically changes these conclusions? Then justify this absurd conclustion.

 

[pervect]

I think it's sufficient to argue that spherical symmetry could exist. It's not like having spherical symmetry breaks any physical laws.

 

[zonde]

Not only Birkhoff's theorem, but the most general spherically symmetric GR solutions simply have the result that a collapsing or oscillating matter that is spherically symmetric does not radiate, so there is no contradiction at all.

You are adding that part about collapsing and oscillating on top of math. This is interpretation of math.

Of course there is no perfect spherical symmetry, but as with much of physics, we use a simple case to get at certain fundamentals.

Yes, we do that all the time.

Do you argue that a slight deviation from such symmetry radically changes these conclusions? Then justify this absurd conclustion.

I think it's sufficient to argue that spherical symmetry could exist. It's not like having spherical symmetry breaks any physical laws.

I will respond to pervect's comment. PAllen, if you think that your question is not addressed by my reply to pervect then please tell.

I would argue that perfect spherical symmetry breaks laws of quantum mechanics.
Let's say we have source of light that is approximately spherically symmetric. It can emit spherical light pulse.
Light can be polarized so it obviously can't be purely longitudinal. Now let's require that this approximately spherical light source is perfectly spherically symmetric. Then we can argue that such lightsource should emit perfectly spherical pulse of light but because perfectly spherical light can be only purely longitudinal wave we arrive at contradiction.

 

[Naty1]

Pallen, PeterDonis:
All the jibber jabber* about null surfaces [which you two agreed upon] got me thinking about some of the details of those...I did some checking in Wikipedia and found:

[*This is Penny's 'technical term' for physicsspeak in THE BIG BANG tv show]

I wasn't aware of this underlying distinction:

Space-like singularities are a feature of non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the following property:
geodesic incompleteness: Some light-paths or particle-paths cannot be extended beyond a certain proper-time or affine-parameter (affine parameter is the null analog of proper time).
It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes, or whether they are artifacts of high symmetry and turn into spacelike singularities when realistic perturbations are added.

http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

Do these two cases lead to different horizons with any different characteristics??

A trapped null surface is a set of points defined in the context of general relativity as a closed surface on which outward-pointing light rays are actually converging (moving inwards). Trapped null surfaces are used in the definition of the apparent horizon which typically surrounds a black hole.

[edit] Definition

We take a (compact, orientable, spacelike) surface, and find its outward pointing normal vectors. The basic picture to think of here is a ball with pins sticking out of it; the pins are the normal vectors.

Now we look at light rays that are directed outward, along these normal vectors. The rays will either be diverging (the usual case one would expect) or converging. Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface.

I think the definition I have seen is consistent with 'outward-pointing light rays are actually converging (moving inwards)..'...Do you guys agree??

Seems like other horizons maybe Rindler, might not meet this 'closed' definition?? Is that correct?? I'm thinking of a Rindler horizon that looks like these:

http://en.wikipedia.org/wiki/Rindler_coordinates#The_Rindler_observers

Thank you

 

[PAllen]

You are adding that part about collapsing and oscillating on top of math. This is interpretation of math.

Let me clarify what what is definition and what is math in the statement that "any spherically symmetric, asymptotically flat GR solution does not radiate energy via gravitational waves". First, no assumptions at all are needed about matter (e.g. no energy condition on the stress energy tensor. No assumptions are needed about vaccuum, other fields, existence of any static regions, etc.

Definition of gravitational radiation energy in an asymptotically flat pseudo-riemannian manifold: the difference between the ADM energy and the Bondi energy. Each of these is a strictly mathematically defined quantity. For example, for a mutually orbiting bodies, the ADM energy remains constant, the Bondi energy is a decreasing function of time, the difference being the energy carried away by the gravitational radiation.

Known theorem: given any asymptotically flat spherically symmetric pseudo-rieamannian manifold (could have non-vanishing Ricci curvature (= stress energy) everywhere, meaning no vaccuum[except in limit at infinity]; could be oscillating, collapsing, whatever ), the ADM energy = Bondi energy. Thus there is no gravitational radiation.

 

[PAllen]

I will respond to pervect's comment. PAllen, if you think that your question is not addressed by my reply to pervect then please tell.

I would argue that perfect spherical symmetry breaks laws of quantum mechanics.
Let's say we have source of light that is approximately spherically symmetric. It can emit spherical light pulse.
Light can be polarized so it obviously can't be purely longitudinal. Now let's require that this approximately spherical light source is perfectly spherically symmetric. Then we can argue that such lightsource should emit perfectly spherical pulse of light but because perfectly spherical light can be only purely longitudinal wave we arrive at contradiction.

Bringing in QM is a red herring to a discussion of predictions of classical theories. However, your argument is strictly classical, so we can ignore that. Trivially, who says we have to consider EM radiation at all (as previously argued, we already know that gravitational radiation won't exist given spherical symmetry)? Obviously, to talk about 'seeing' we need it, but then it can be introduced in the same approximate sense we talk about test bodies - light follows null geodesics, and we don't inquire into its details (e.g. we haven't been talking about the energy carried away from a collapsing body by the light allowing us to see it; we blithely assume we can make this as insignificant as desired).

To model light as an EM field in GR, we have to consider a stress energy tensor that is not vacuum anywhere - E and B fields contribute to the stress energy tensor. So we are talking about something very different from your ideal SC case if these contributions are significant. Then, I believe it does follow that there are no exactly spherically symmetric solutions. However the deviations from spherical symmetry can be made as small as desired, and no conclusions we've been discussing would be affected.

In short, classically this is a red herring as well.So far as I see, you have not offered an substantive argument against the conclusions from Birkhoff's theorem that a collapsing spherical shell could have an apparent horizon while the interior of the shell is still empty (and this would be true for any choices for surfaces of simultaneity that go inside the SC radius).

 

[PeterDonis]

To model light as an EM field in GR, we have to consider a stress energy tensor that is not vacuum anywhere - E and B fields contribute to the stress energy tensor. So we are talking about something very different from your ideal SC case if these contributions are significant. Then, I believe it does follow that there are no exactly spherically symmetric solutions.

There are no exactly spherically symmetric solutions for EM *radiation*; the lowest order radiation is dipole. The Wiki page on null dust solutions has a good overview of the types of spacetimes that contain "radiation":

http://en.wikipedia.org/wiki/Null_dust_solution

There is an exactly spherically symmetric solution with a nonzero EM field: Reissner-Nordstrom spacetime, which has a purely radial electric field. But there is no EM radiation in that spacetime; it is static.

 

[PAllen]

There are no exactly spherically symmetric solutions for EM *radiation*; the lowest order radiation is dipole. The Wiki page on null dust solutions has a good overview of the types of spacetimes that contain "radiation":

http://en.wikipedia.org/wiki/Null_dust_solution

There is an exactly spherically symmetric solution with a nonzero EM field: Reissner-Nordstrom spacetime, which has a purely radial electric field. But there is no EM radiation in that spacetime; it is static.

I thought it was clear that I was referring to solutions with radiation, since that was the issue Zonde raised. However, it never hurts to clarify.

 

[PAllen]

This paper suggests it should be perfectly possible to have spherically symmetric collapse with outgoing null radiation (which can represent incoherent light):

http://arxiv.org/pdf/gr-qc/0504045v1.pdf

This particular construction specifies ingoing radiation (incoming Vaidya metric), but it seems very likely to me that you could match outgoing Vaidya to collapsing dust using similar methods. This would be a perfectly spherically symmetric solution.

 

[PeterDonis]

This paper suggests it should be perfectly possible to have spherically symmetric collapse with outgoing null radiation (which can represent incoherent light):

http://arxiv.org/pdf/gr-qc/0504045v1.pdf

This particular construction specifies ingoing radiation (incoming Vaidya metric), but it seems very likely to me that you could match outgoing Vaidya to collapsing dust using similar methods. This would be a perfectly spherically symmetric solution.

Hm, good point, the Vaidya null dust is spherically symmetric (I think both ingoing and outgoing are). But the Vaidya null dust does not directly model any "source" for the radiation; you can match it to collapsing matter, as this paper does, but that doesn't really explain how the matter radiates. In particular, I don't believe the Vaidya null dust is derived by solving the combined Einstein-Maxwell equations, so it doesn't necessarily represent a physically reasonable source for EM radiation. But you're right, it is a spherically symmetric metric with radiation present.

 

[PeterDonis]

Do these two cases lead to different horizons with any different characteristics??

The horizon of a charged or rotating BH (both of which have timelike singularities in the idealized case of exact symmetry) does have some different characteristics from that of an uncharged, nonrotating BH (which has a spacelike singularity in the idealized case). However, they're not that much different, certainly not as different as the singularities are. AFAIK the speculation about the timelike singularities not being stable under perturbations does not apply to their corresponding horizons; I believe the horizons themselves are thought to be physically possible, it's just what's hidden deeper inside them that may be very different from the idealized case.

I think the definition I have seen is consistent with 'outward-pointing light rays are actually converging (moving inwards)..'...Do you guys agree??

I do, yes.

Seems like other horizons maybe Rindler, might not meet this 'closed' definition?? Is that correct??

I think so; I don't think it's possible to find a closed 2-surface that is contained in the Rindler horizon, because the motion of the family of observers that define the horizon is not spherically symmetric. In any case, the Rindler horizon is not a trapped null surface (it's null, but it's not trapped).

 

[PAllen]

Hm, good point, the Vaidya null dust is spherically symmetric (I think both ingoing and outgoing are). But the Vaidya null dust does not directly model any "source" for the radiation; you can match it to collapsing matter, as this paper does, but that doesn't really explain how the matter radiates. In particular, I don't believe the Vaidya null dust is derived by solving the combined Einstein-Maxwell equations, so it doesn't necessarily represent a physically reasonable source for EM radiation. But you're right, it is a spherically symmetric metric with radiation present.

It can't possibly represent an exact EM solution for the very reason that even in SR there are no point sources of radiation, only dipole or higher. At a distance, for all practical purposes, you can treat spherical wave front, but not if we are discussing exact spherical symmetry.

However, the Vaidya null dust outgoing radiation could model e.g. massless neutrinos or the like. However, your point about source still remains. You would have to treat it as a causeless source of information about the boundary between matter and 'radiation'.

In any case, the main point is that real world difficulties with exact spherical symmetry does not impede making reasonable conclusions from artificial exact cases. It's one thing to note that the internal region approaching the singularity is likely very inaccurate in the same sense as suggesting that a ring of sharpshooter firing together is a useful way to manufacture canonballs (as opposed to collective suicide). However, in both cases, away from the very center, spherical symmetry is a useful approximation, and there is no reason I know of (or proposed) to doubt general conclusions about horizon formation (here I am talking to Zonde - I know you agree).

 

[zonde]

PAllen,
But do you agree that putting in restriction that there is (asymptotically) no EM radiation is statement about matter configuration?

 

[PAllen]

PAllen,
But do you agree that putting in restriction that there is (asymptotically) no EM radiation is statement about matter configuration?

Not really. Putting in realistic amounts of light emission with infinitesimal deviations from spherical symmetry would greatly complicate the math but not change any of the main conclusions we're drawing in this thread. Note, that you have freely argued from SC coordinates even though they are just one coordinate system on the most perfectly simple geometry, whenever it suits your purpose - which is fine, as long you don't attach significance to the specialized features which would not generalize to realistic situations.

 

[my_wan]

I think that the utility of examples with free falling observers dries up at the moment when you try to construct global coordinate system where some background stays more or less static, isotropic and homogenous.

I certainly was not trying to imply some specific "utility" of "free falling observers". I was pointing out that the definition of an event horizon suffered the same limited utility issues that free falling observers do.

It appears to me that you are implying that "free falling observers" lack a certain utility while "event horizons" retain said utility, even though the definition of the "event horizon" itself is an observer dependent construct. Perhaps you intended something more nuanced but, so far as I can see, this is what you implied.

Tidal forces are not exclusively associated with event horizon. Tidal forces are present in any field of gravity.

Really! I thought it was quantum fluctuations.. Just kidding, of course tidal forces are common to all gravitational bodies.

This assumption is problematic if you are trying to construct an argument about possible formation of black hole.
Look up Begging the question fallacy.

Which question is it begging here? It's a matter of historical fact that black holes where theoretical entities long before Einstein. If you thought I "assumed" photons have mass you are wrong. This was merely an assumption that existed before Einstein and QM, on which pre-Einstein black holes were theoretically predicated on. The only feature required to qualify as a black hole is that light can't escape. I was stating a historical fact, not making any claim, or assumption, we know today to be invalid.

 

[zonde]

Not really. Putting in realistic amounts of light emission with infinitesimal deviations from spherical symmetry would greatly complicate the math but not change any of the main conclusions we're drawing in this thread.

Basically you think (believe) that there are no factors that can oppose runaway gravitational collapse given big enough mass, right?

Maybe we can end our discussion there? Your replays where very good but we have to stop somewhere.

 

[PAllen]

Basically you think (believe) that there are no factors that can oppose runaway gravitational collapse given big enough mass, right?

Maybe we can end our discussion there? Your replays where very good but we have to stop somewhere.

Fine, but one slight qualification: I think that is what GR predicts. I do not believe singularities actually form, and I have doubts about the exact nature of event horizons. I distinguish understanding what GR predicts, as a classical theory, from what is likely true in our universe - that GR breaks down in certain regimes, just as Maxwell's equations do.

 

[pervect]

Basically you think (believe) that there are no factors that can oppose runaway gravitational collapse given big enough mass, right?

Maybe we can end our discussion there? Your replays where very good but we have to stop somewhere.

As far as I can tell, (I have only been skimming the thread, because from what I've read it hasn't been going anywhere) the discussion isn't actually about this issue, but it's about something simpler, which is whether there are any factors that can prevent the formation of an event horizon.

And it's pretty clear that the answer to that (in the literature) is no.

 

[zonde]

It appears to me that you are implying that "free falling observers" lack a certain utility while "event horizons" retain said utility, even though the definition of the "event horizon" itself is an observer dependent construct. Perhaps you intended something more nuanced but, so far as I can see, this is what you implied.

If we speak about event horizon as closed surface then we want some global coordinate system. And it seems to me (but you can dispute this) that in any viable global coordinate system event horizon keeps it's place.

Which question is it begging here? It's a matter of historical fact that black holes where theoretical entities long before Einstein. If you thought I "assumed" photons have mass you are wrong. This was merely an assumption that existed before Einstein and QM, on which pre-Einstein black holes were theoretically predicated on. The only feature required to qualify as a black hole is that light can't escape. I was stating a historical fact, not making any claim, or assumption, we know today to be invalid.

I didn't mean assumption that we can model such gravity field that light can't escape. I rather meant assumption that there exists (can form) gravitating object with such gravity field.

 

[zonde]

My intention about this thread was to check out if formation of black hole does not require pre-existing micro black hole. And it seems I got an answer. Apparent event horizon can form at once and as I consider it physically meaningful contrary to absolute horizon it is the answer to my question - pre-existing micro black hole is not required.

 

[my_wan]

If we speak about event horizon as closed surface then we want some global coordinate system. And it seems to me (but you can dispute this) that in any viable global coordinate system event horizon keeps it's place.

You have effectively just defined all possible coordinate systems as on-viable.

I didn't mean assumption that we can model such gravity field that light can't escape. I rather meant assumption that there exists (can form) gravitating object with such gravity field.

So I get from this you don't believe black holes exist. Nothing wrong with questioning their legitimacy, in whole or in part, but to simply deny their existence is just as wrong as an insistence they must exist a priori. Given our observational data at present denying the possibility of such an assumption requires some major contortions of logic.

 

[zonde]

So I get from this you don't believe black holes exist. Nothing wrong with questioning their legitimacy, in whole or in part, but to simply deny their existence is just as wrong as an insistence they must exist a priori. Given our observational data at present denying the possibility of such an assumption requires some major contortions of logic.

We have theoretical concept called "black hole" and we have observed objects that we call "black holes". Both things got the same name ... logically it is the same thing, right?
Is this how you think?

 

[my_wan]

We have theoretical concept called "black hole" and we have observed objects that we call "black holes". Both things got the same name ... logically it is the same thing, right?
Is this how you think?

I'm quiet willing to entertain the notion that the things we observe and label "black holes" may not strictly be the things we describe them to be. However, only a single property is required to keep the label "black hole", that being that light cannot escape its interior.

In spite of this willingness to entertain alternative descriptions of what we are observing, it's going to require something far more specific than a rejection of the standard description to be of interest.

 

[zonde]

I'm quiet willing to entertain the notion that the things we observe and label "black holes" may not strictly be the things we describe them to be. However, only a single property is required to keep the label "black hole", that being that light cannot escape its interior.

There shouldn't be anything that can escape it's interior to call it "black hole".

In spite of this willingness to entertain alternative descriptions of what we are observing, it's going to require something far more specific than a rejection of the standard description to be of interest.

So you do not take answer "we don't know" as acceptable, right?

 

[my_wan]

So you do not take answer "we don't know" as acceptable, right?

If we did factually know I wouldn't be willing to entertain alternative models of our observations. Hence your presumption of what I find acceptable is most definitely in error. I also spend some time arguing how we can't be as certain about many things as we tend to like to believe, on a wide variety of issues.

If you want to reject BH physics as we know it fine. I entertain all kinds of wild ideas for creative reasons. If you want to convince anybody else you need a far more specific argument than "we don't know". Among those issues that needs to be addressed, which I think PAllen's approach was an admirable attempt at doing, is how you can think a global coordinate system can be selected that is somehow more meaningful than what can be provided by the observations of a free falling observer. A coordinate system is, by definition, an observer construct. Even what constitutes a "closed surface" is an observer dependent construct. You can't cling to one while rejecting the other, at least not without making some fundamental arguments that go well beyond just BH physics.

 

[zonde]

If we did factually know I wouldn't be willing to entertain alternative models of our observations. Hence your presumption of what I find acceptable is most definitely in error. I also spend some time arguing how we can't be as certain about many things as we tend to like to believe, on a wide variety of issues.

If you want to reject BH physics as we know it fine. I entertain all kinds of wild ideas for creative reasons. If you want to convince anybody else you need a far more specific argument than "we don't know".

Hmm, maybe you have just misunderstood me. I was not trying to argue against BH with this "Begging the question" argument. I was just saying that some arguments defending BH are better than others.

If you want arguments against BH then state that question so that I know about what we are talking.

 

[my_wan]

Hmm, maybe you have just misunderstood me. I was not trying to argue against BH with this "Begging the question" argument. I was just saying that some arguments defending BH are better than others.

If you want arguments against BH then state that question so that I know about what we are talking.

And all I was pointing out, when you responded with the 'begging the question' response, was that even in the absents of GR theoretical grounds remain for the existence of lack holes. Hence any argument against them must be more expansive than the issues GR alone dictates. This was in turn predicated on what you said you wanted to discuss, which said: "1. Assume that BH exists."

Let's assume the opposite, such that they don't exist. This means, irrespective of GR, there no regions of spacetime which light can't escape. This entails an absolute limit in the potential change in depth of a gravitational field.

The only way I know to attempt this is to assume the relative mass (not necessarily proper mass) decreases as the gravitational depth increases, such that a collapsing body can only asymptotically approach the creation of an event horizon. Much the same way an accelerated mass can only asymptotically approach the speed of light. In such a case, light would still escape, but even x-rays would escape at such long wavelengths (low energy) as to effectively be radio waves to the external observer.

If you assume the Nordtvedt effect is valid, and the Strong Equivalence Principle is violated, then that would cut short such an argument. However, no evidence of such a violation exist. You can then try to impose such a limit, but that still requires that the proper mass of the material making up the black hole has no direct observational meaning for an external observer. Much like the apparent mass increase in GR, as a mass decreases its gravitational depth, or its binding energy is reduced. This would also imply that the 'proper' mass has no more absolute meaning than any other arbitrarily chosen relativistic measure.

Is that the kind of argument you wanted to discuss?

 

[zonde]

And all I was pointing out, when you responded with the 'begging the question' response, was that even in the absents of GR theoretical grounds remain for the existence of lack holes. Hence any argument against them must be more expansive than the issues GR alone dictates. This was in turn predicated on what you said you wanted to discuss, which said: "1. Assume that BH exists."

I wanted to discuss PAllens example with collapsing cluster of stars. And I tried to explain why I consider it better than other examples (with observers in free fall). And the difference is that in PAllens example we do not assume anything about existence/non-existence of BH. We just play the situation forward according to our understanding of physical laws.

Let's assume the opposite, such that they don't exist. This means, irrespective of GR, there no regions of spacetime which light can't escape. This entails an absolute limit in the potential change in depth of a gravitational field.

The only way I know to attempt this is to assume the relative mass (not necessarily proper mass) decreases as the gravitational depth increases, such that a collapsing body can only asymptotically approach the creation of an event horizon. Much the same way an accelerated mass can only asymptotically approach the speed of light. In such a case, light would still escape, but even x-rays would escape at such long wavelengths (low energy) as to effectively be radio waves to the external observer.

If you assume the Nordtvedt effect is valid, and the Strong Equivalence Principle is violated, then that would cut short such an argument. However, no evidence of such a violation exist. You can then try to impose such a limit, but that still requires that the proper mass of the material making up the black hole has no direct observational meaning for an external observer. Much like the apparent mass increase in GR, as a mass decreases its gravitational depth, or its binding energy is reduced. This would also imply that the 'proper' mass has no more absolute meaning than any other arbitrarily chosen relativistic measure.

Hmm, but why would you associate this with Nordtvedt effect. Strong Equivalence Principle can hold just the same. I can say that inertial mass=active gravitating mass=passive gravitating mass is reduced.

And I see another possibility what can prevent BH formation. It is degeneracy of matter.

 

[my_wan]

I mentioned the Nordtvedt effect because if it held, which is pretty unlikely, such that the gravitational self-energy contributed to its total gravitational mass, then you can't get a relativistic reduction of gravitational mass for an external observer, since even if the inertial mass is reduced its gravitational mass would remain. That's why it would violate the strong equivalence principle. I don't take this effect seriously, but it would render the scenario I described as moot.

I'm not sure how degenerate matter can be exploited to prevent BH formation. In PAllen's scenario the matter density never even observably got especially dense in any local sense. Even in the event it did, you still have to presume the Fermi-pressure would grow indefinitely as the total gravitational pressure increased. Possible I suppose, but fails completely in PAllen's scenario.