Graphical example of BH formation by PAllen

zonde

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

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

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.

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

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

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

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

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

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

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 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

[QUOTE=PAllen;4086623]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).

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

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

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

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.

PAllen

LQG is a successor to GR. It definitely assumes GR is true only in a limited domain. This is also what I believe is true of the universe, but that is not relevant to a discussion of what GR predicts.

TrickyDicky

Hmmm.. this is a tricky position...in a limited domain? how limited and who decides where the limit is? Just asking so I know what predictions of GR should I take seriously.

PAllen

My personal opinion? Somewhere near the singularity - e.g. when the mass/energy is near Planck temperature; and also that the event horizon is not really a horizon at the microscopic quantum level, but macroscopically is very close in behavior to GR predictions.