Graphical example of BH formation by PAllen

[zonde]

PAllen,
How vital is concept of absolute horizon for this discussion (formation of black hole)?
Isn't it possible to define black hole using apparent horizon? At least in some specific cases if not all?

 

[PeterDonis]

You are talking past the statement you quoted.

Definition of horizon is question about picking out particular null surface from other null surfaces as special.

Yes. So what? It's still a null surface, and you can still translate any statement about the horizon "existing" at a particular "time" into a statement about the particular null surface that is the horizon intersecting a particular spacelike surface.

 

[PAllen]

PAllen,
How vital is concept of absolute horizon for this discussion (formation of black hole)?
Isn't it possible to define black hole using apparent horizon? At least in some specific cases if not all?

Sure you can choose not to worry about the true horizon. Once a black hole is stable, with no more matter falling in for for quite a while, they coincide to any limit of measurement. Apparent horizons are more complex to derive for the scenarios under discussion. However, we can say the following:

1) For the collapsing spherical shell, by the time the the shell is inside its SC radius, the apparent horizon is at the SC radius. At this time (as observed by interior observers), there is not yet any singularity, nor (necessarily) any high density of matter (if the shell is enormous enough). Note, it is guaranteed that a singularity will form as the shell cannot stop collapsing at this point. (per GR of course).

2) For the collapsing star cluster, a similar observation is true. As soon as the cluster is within its SC radius, we know the apparent horizon is at the SC radius. There is no requirement that any stars have collided, nor any singularity exist yet (for interior observers). Again, per GR, it is guaranteed that a singularity will form.

The only thing I can't fill in (with my available time and resources) is the early history of the apparent horizon in these two scenarios. The true horizon is easier to derive general features of using general principles.

 

[zonde]

1) For the collapsing spherical shell, by the time the the shell is inside its SC radius, the apparent horizon is at the SC radius.

Let's take a closer look at SC solution and how much does it applies to collapsing body.
SC solution describes gravity around static (existing in equilibrium state) body. Now we take series of SC solutions with the same mass and progressively smaller radius. As mass is the same and radius shrinks it seems like we can claim that this series of SC solutions describes collapsing body.
But each solution for certain radius describes static body. And in order for the same body to go from larger radius to smaller radius and then reach equilibrium state at smaller radius it should release binding energy (reducing it's mass by appropriate amount). And that makes quite different series of SC solutions.

So in order to claim that this series of SC solutions with the same mass and progressively smaller radius describe collapsing body we have to assume equivalence between
compressed smaller body (less particles) that has not yet released binding energy
and
bigger body (more particles) at the same radius that has already released binding energy.

Does it make sense so far?

 

[PAllen]

Let's take a closer look at SC solution and how much does it applies to collapsing body.
SC solution describes gravity around static (existing in equilibrium state) body. Now we take series of SC solutions with the same mass and progressively smaller radius. As mass is the same and radius shrinks it seems like we can claim that this series of SC solutions describes collapsing body.
But each solution for certain radius describes static body. And in order for the same body to go from larger radius to smaller radius and then reach equilibrium state at smaller radius it should release binding energy (reducing it's mass by appropriate amount). And that makes quite different series of SC solutions.

So in order to claim that this series of SC solutions with the same mass and progressively smaller radius describe collapsing body we have to assume equivalence between
compressed smaller body (less particles) that has not yet released binding energy
and
bigger body (more particles) at the same radius that has already released binding energy.

Does it make sense so far?

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.

 

[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.

 

[zonde]

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.

So are you saying that I misunderstood you? You was presenting kind of possible (not very strong) argumentation against mass reduction by binding energy?

 

[my_wan]

I was asking if that was the kind of argument you had in mind back in the opening post, where you also characterized "Assume that BH exists" as begging the question. Limiting the creation of black holes through mass reduction by binding energy would be ruled out by the Nordtvedt effect. I only mentioned it to be inclusive of possibilities that contradicted the mechanism I described. Since I don't take the Nordtvedt effect very seriously it actually strengthens the argument. Apparently the answer is no, given your responses.

Consider the apparent relative mass increase of a planet like Mercury, as defined by GR, at its aphelion compared to its perihelion. Conversely a mass minimum at its perihelion. Hence the total relative mass apparently decreases as the mass density increases. For a far removed observer, wouldn't this then indicate that the total relative mass of the system varies inversely with density? This then implies that for a given constant volume of space, as defined by some external observer, the addition of masses to this volume would then add up in a manner similar to the relativistic addition of velocities, as seen by the external observer.

This wouldn't necessarily invalidate an event horizon, for the same reason that an apparent horizon can be present in a particle's accelerating reference, beyond which events are unobservable. This actually makes it possible to accelerate fast enough to prevent a photon from ever catching you.

Anyway, I started thinking about this in response to your apparent objection to assuming black holes exist. Because if your going to object to that assumption some mechanism for avoiding them is required. "We don't know", however valid in general, is not sufficient when specific mechanism are required to avoid black holes.

 

[zonde]

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.

This is rather complicated topic and I would like to discuss it only if we can dedicate some time for that topic alone.

Consider the apparent relative mass increase of a planet like Mercury, as defined by GR, at its aphelion compared to its perihelion. Conversely a mass minimum at its perihelion. Hence the total relative mass apparently decreases as the mass density increases. For a far removed observer, wouldn't this then indicate that the total relative mass of the system varies inversely with density? This then implies that for a given constant volume of space, as defined by some external observer, the addition of masses to this volume would then add up in a manner similar to the relativistic addition of velocities, as seen by the external observer.

I can't consider this scenario. I don't know how to model it.
And I am not sure about the term "relative mass". I imagined it as something like proper mass minus binding energy, is this in the right direction? But then I don't know how it can be represented in GR as I don't know how (or if) binding energy is represented in GR.

Anyways I know we can speak about binding energy as we compare one equilibrium state with another equilibrium state. But I'm not sure how to model dynamics between equilibrium states in respect of binding energy. And certainly aphelion and perihelion of Mercury are not equilibriums states for the whole system.

 

[zonde]

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.

Okay one question is what happens when matter is degenerate but you try to contain it within some volume. I think that degenerate matter can not be contained by other particles i.e. it does not participate in elastic collisions. I am not sure if I can propose solid arguments why it should be so from perspective of QM. The problem is with interpretation of "quantum state" in case of free particles. Anyways we can speculate that this is the case with neutrinos - they are very degenerate and after encounter with other particles they fall back on the same trajectory (the same momentum/position state) as before collision with very high probability.

Speaking about degeneracy and density dependence. To claim that the two are varying proportionally we have to assume that there is some cut-off distance for quantum level occupancy, meaning that particles don't compete for quantum state given sufficient distance. However we can assume that this "quantum level occupancy" effect drops as inverse square law. And in this case density factor does not exactly determine degeneracy level and it is more related to number of particles and distance to them.
And assuming this PAllen's scenario is still subject to questions about degeneracy levels as number of particles is much higher even so the distances are bigger as well.

 

[PAllen]

Okay one question is what happens when matter is degenerate but you try to contain it within some volume. I think that degenerate matter can not be contained by other particles i.e. it does not participate in elastic collisions. I am not sure if I can propose solid arguments why it should be so from perspective of QM. The problem is with interpretation of "quantum state" in case of free particles. Anyways we can speculate that this is the case with neutrinos - they are very degenerate and after encounter with other particles they fall back on the same trajectory (the same momentum/position state) as before collision with very high probability.

Speaking about degeneracy and density dependence. To claim that the two are varying proportionally we have to assume that there is some cut-off distance for quantum level occupancy, meaning that particles don't compete for quantum state given sufficient distance. However we can assume that this "quantum level occupancy" effect drops as inverse square law. And in this case density factor does not exactly determine degeneracy level and it is more related to number of particles and distance to them.
And assuming this PAllen's scenario is still subject to questions about degeneracy levels as number of particles is much higher even so the distances are bigger as well.

So, you propose two stars 10 million miles apart are fine, but add more, further away, there is a problem of quantum occupancay? It would be a wild theory, different from any currently known, to have such an effect. Which all gets back to: you can say BH don't form if and only if you admit you say GR is seriously wrong. Which is fine, but be willing to say it.

 

[zonde]

you can say BH don't form if and only if you admit you say GR is seriously wrong.

It would be nice to be as confident as you are ... but I am not.

Say I have heard that particles without any forces applied to them follow geodesics. But as I look more into details it turns out it is an approximation. You have to assume that particle has zero (negligible) mass.
So maybe you can tell me (if you know) - when we take into account particle's own gravity in what (space-time) direction it deviates from original geodesic (if we speak about particle falling radially toward gravitating mass)?

 

[PAllen]

It would be nice to be as confident as you are ... but I am not.

Say I have heard that particles without any forces applied to them follow geodesics. But as I look more into details it turns out it is an approximation. You have to assume that particle has zero (negligible) mass.
So maybe you can tell me (if you know) - when we take into account particle's own gravity in what (space-time) direction it deviates from original geodesic (if we speak about particle falling radially toward gravitating mass)?

It won't change direction. It will emit some amount of gravitational radiation and slow down (assuming the initial configuration had exactly zero angular momentum).

Let's turn it around: on what basis are your doubts about what GR predicts (as opposed to any beliefs about reality)? Note that we have the following:

- artificially perfect exact solutions showing formation of black holes
- theorems with very weak assumptions showing black hole formation is inevitable under general, realistic conditions
- ever more precise numeric simulations of black hole formation
- no theoretical counter arguments I've seen that don't actually modify GR (e.g. incorporating some model of quantum correction).

Note, even your argument about quantum occupancy is an argument that GR is incorrect, since such cannot be represented in a stress energy tensor, and cannot be described classically. If your actual argument is that there exist approaches to apply quantum arguments to GR that avoid singularities and event horizons, this is a no brainer. I can link dozens of such arguments, some may be close to how the world works, but none are statements about what GR predicts as a classical theory; all are modifications of GR in the same spirit as QED is to Maxwell EM.

 

[zonde]

It won't change direction. It will emit some amount of gravitational radiation and slow down (assuming the initial configuration had exactly zero angular momentum).

Let's turn it around: on what basis are your doubts about what GR predicts (as opposed to any beliefs about reality)?

I have doubts about exactness of GR predictions. It's too open for interpretation.

Note that we have the following:

- artificially perfect exact solutions showing formation of black holes

Are there any exact solution for runaway gravitational collapse? No? Then you can't claim that.
Obviously you need such a solution to claim that massive body undergoing runaway gravitational collapse and not emitting gravitational waves is a valid solution to EFE.

EFE take as arguments continuous 4D tensor fields. I simply do not get why I should believe it's something calculable without radical approximations.

You need coordinate system to express continuous tensor field. And this coordinate system is supposedly defined using this same tensor field. To me it seems like circular definition.

Hyperbolic coordinates is a dirty cheat unless you can provide a very serious arguments why they should be considered physically meaningful. So I do not believe argument about coordinate singularity in SC coordinates is valid (as I see "frozen star" is equivalent to "exterior of black hole").

Not to mention that I still don't know how binding energy can be represented in GR. And I consider it important in order to understand GR.




So make your pick.

 

[PAllen]

I have doubts about exactness of GR predictions. It's too open for interpretation.

You could say this about quantum mechanics, QFT, etc. It is a vacuous statement without specific arguments.

Are there any exact solution for runaway gravitational collapse? No? Then you can't claim that.

Sure there are. It's just that the exact ones are implausibly symmetric. How is this different from many other theories where approximation is required for realistic cases?

Obviously you need such a solution to claim that massive body undergoing runaway gravitational collapse and not emitting gravitational waves is a valid solution to EFE.

.
GW emission is expected for any collapse in the real world. Not sure why you thought otherwise. It is only known (mathematically) not to occur for perfect spherical symmetry, which will never exist in the real world. For realistic scenarios, we have (at least) 4 strong reasons to say GR predicts black holes, and you have still not provided a single reason for believing GR does not:

(1) simple, exact solutions (considered as indicative of general features of more realistic cases)
(2) general singularity theorems
(3) absence of any process with GR + classical matter models + reasonable quantum models that could prevent super massive BH formation (that is, matter coalescing within the horizon radius; any type of horizon you like).
(4) numeric models of ever growing sophistication (these, for example, model the precise GW emission spectrum expected from realistic collapses).

EFE take as arguments continuous 4D tensor fields. I simply do not get why I should believe it's something calculable without radical approximations.

see above

You need coordinate system to express continuous tensor field. And this coordinate system is supposedly defined using this same tensor field. To me it seems like circular definition.

This makes no sense to me. You need coordinate charts to define manifold topology. You do not define a coordinate system from a tensor field. This circularity is your invention or misunderstanding.

Hyperbolic coordinates is a dirty cheat unless you can provide a very serious arguments why they should be considered physically meaningful. So I do not believe argument about coordinate singularity in SC coordinates is valid (as I see "frozen star" is equivalent to "exterior of black hole").

1) So you reject 'general covariance' or diffeomorphism invariance: a definitional principle of GR. This is completely equal to the statement that you reject GR, which for some reason you are unwilling to admit.
2) Are you aware that you can derive the Kruskal metric directly from the EFE without ever introducing the SC coordinates? (I'm guessing that by hyperbolic coordinates you mean Kruskal).
3) Lemaitre coordinates are not hyperbolic and have no horizon singularity, and can also be derived directly from the EFE.

Not to mention that I still don't know how binding energy can be represented in GR. And I consider it important in order to understand GR.

1) To the extent this argument is valid, it is an argument against the validity of GR, which for some reason you remain resistant to admit.

2) In any case, GR says plenty about binding energy, but there are loose ends and open issues. First, in any asymptotically flat spacetime, there is globally conserved energy. Binding energy for non-catastrophic collapse is modeled by emission of ordinary radiation + GW. It is true that without an asymptotic geometry assumption, GR cannot account for total energy conservation, and that none of quasi-local approaches is fully satisfactory. However, for practical purposes, you can take a sufficiently isolated region, and model it as if it were embedded in asymptotically flat spacetime. To the extent this is a cheat (and it is, technically), your issue is with GR itself. Another anomaly of GR itself is that catastrophic collapse is predicted to be irreversible to an extent beyond what can be explained with binding energy (e.g. the Oppenheimer-Snyder collapse emits no radiation at all (GW or regular), yet is irreversible in the sense that you can't continue the forward time solution from after the horizon forms to a re-expansion without violating the EFE. Note, within the Lemaitre-Tolman generalization of Oppenheimer-Snyder, you can have WH->BH solutions but not BH->WH solutions. Time reverse WH->BH and you still have WH->BH.)

 

[TrickyDicky]

1) So you reject 'general covariance' or diffeomorphism invariance: a definitional principle of GR. This is completely equal to the statement that you reject GR, which for some reason you are unwilling to admit.

Then many relativists "reject GR", because there is an unsolved controversy (mostly from the LQG people) about what exactly is "general covariance" for dynamical theories.