Black hole mass coupled to expansion -- astrophysical source of dark energy?

[PeterDonis]

The conventional black hole has mass, angular momentum, and charge

Yes.

all of which are at or within the event horizon

No. All three of these are global properties of the spacetime geometry. There is no location you can point to in the spacetime and say that that is "where" the mass, angular momentum, or charge are. That is why physicists are careful to define all of those quantities in terms of external measurements at infinity (or at least very far away).

 

[.Scott]

No. All three of these are global properties of the spacetime geometry. There is no location you can point to in the spacetime and say that that is "where" the mass, angular momentum, or charge are. That is why physicists are careful to define all of those quantities in terms of external measurements at infinity (or at least very far away).

Would the "stress-energy" created by Dark energy also be a global property of the spacetime geometry?

 

[PeterDonis]

Would the "stress-energy" created by Dark energy also be a global property of the spacetime geometry?

No. In the proposed model, the interior of the objects is not vacuum, as it is in a standard black hole; the interior contains the dark energy that was created from the collapsing matter by some sort of phase transition (that conversion process stops the collapse). But the mass of the object (and its angular momentum and charge, if any) would be a global (sort of--see below) property of the spacetime geometry.

Also bear in mind that "global property of the spacetime geometry" assumes we are talking about a single isolated black hole (or object like those in the proposed model). In a universe consisting of a huge number of such objects, "global" when referring to the mass, angular momentum, and charge of a single object really means something like "the region of spacetime that is closer to this particular object than to any other objects". The point is that properties like mass, angular momentum, and charge cannot be localized to a particular place inside the object.

 

[Ken G]

I mean that, simply due to local conservation of stress-energy, a phase transition inside the collapsing matter during the collapse cannot change the externally measured mass.

Yes, the mass change is over time. But so is the dark energy appearance.

Yes, but that's not due to the collapse process, it's due to a claimed coupling with the overall expansion of the universe. That coupling only comes into play on time scales much longer than the collapse time scale.

I agree, the mass increase, and therefore the appearance of the dark energy effect, comes from coupling to the acceleration. But the acceleration also comes by coupling to the dark energy, so neither leads the other, they must both emerge together in a weird kind of bootstrapping. What is missing from that kind of argument, however, is a demonstration of why that overall coupled solution is the preferred one, instead of something else that also seems like it could happen (like a non-accelerating solution with normal black holes). To really say there is an explanation for dark energy, that added piece would need to be developed (along with your point that these solutions survive the necessary spatial averaging). My sense on that last one is, spatial averaging should not be too much of a challenge to the idea, given that the whole thing rests on some spectacularly long-range effects-- it is the long-range aspect itself that seems like a problem.

That's correct, but if dark energy is not created inside the object, then there's nothing for the claimed coupling described above to work on. Ordinary collapsing matter does not contain any dark energy. So at some point during the collapse process, the ordinary collapsing matter has to somehow be converted to dark energy (i.e., some kind of phase transition has to occur) in order for the claimed coupling to have the effects it is claimed to have.

That does seem to be a way to picture what they are saying, but I'm saying it cannot go in a sequence, normal matter converts to dark energy during accretion, and then all that dark energy causes the acceleration. The acceleration must provide the coupling that "causes" the phase transition, so the matter inside the black hole has to in some sense "wait for" the acceleration to proceed, which causes some of it to gradually undergo this putative phase transition to dark energy, which then causes more acceleration, and so on to the bootstrapping.

It's not even clear that one has to regard the energy inside the black hole to change form in some sense, it might just be something about being inside a black hole that allows it to increase in mass in the presence of distant expansion acceleration. I believe they are saying that any time the black hole mass has the effect of increasing in proportion to the volume of the universe, then it will act like dark energy, without even needing to be dark energy, in the sense that all "dark energy" ever did was be an energy that increases in proportion to the volume of the universe. (But I don't know enough about the GR to claim that this doesn't require the energy have some weird quality to it that would involve a phase transition of some kind, or even if it is necessary to attribute any properties to the energy inside the black hole at all.)

 

[Ken G]

I would describe it as an "apparent coupling". Since they have excluded "no coupling" to a confidence of 99.98%, either there's something very misleading in the data collection or we're very lucky (or unlucky) in spotting a well-formed pattern from random data.

Probably the former, if their model isn't right. The data they analyzed is not new data, yet the signal they are claiming to detect has never been seen before, in that same data. Granted people didn't know to look for it, but they could be fooling themselves in how they are doing the interpreting. The problem is, it is only easy to get the mass of a distant supermassive black hole when it dominates the signal, and it is only easy to get the stellar mass when there is not a supermassive black hole dominating the signal, but here they need to reliably get both at the same time with no spurious artifacts or biases. So I don't think anybody would say there is a 99.98% chance they are right, only that they cannot be wrong because of random statistics, it has to be some kind of systematic problem in their analysis. We either need independent analysis, or better yet, new data collection that is specifically designed to test the hypothesis. Still, it's certainly a tantalizing idea since it resolves several independent problems at once.

 

[PeterDonis]

the mass change is over time. But so is the dark energy appearance.

Not the initial appearance of dark energy, no; that happens, as I said, as some kind of phase transition inside the collapsing matter when it first collapses. That initial appearance of dark energy is what enables the claimed coupling with expansion to work.

Once the initial dark energy is there (having been converted from the ordinary matter that collapsed), it then increases over time as a result of the claimed coupling with expansion. At least, that's my understanding of the model being proposed.

the mass increase, and therefore the appearance of the dark energy effect, comes from coupling to the acceleration

As far as I can tell, the claimed coupling is just to the expansion, not to acceleration.

normal matter converts to dark energy during accretion

Yes, but that dark energy then increases due to the claimed coupling with expansion. See above.

all that dark energy causes the acceleration

Yes, all of it, both the dark energy that was initially created during the collapse process, and the additional dark energy that gets added via the coupling with expansion.

It's not even clear that one has to regard the energy inside the black hole to change form in some sense, it might just be something about being inside a black hole that allows it to increase in mass in the presence of distant expansion acceleration.

No, it can't, because there is nothing inside an ordinary black hole that does this. That's why a different model of what these objects actually are, with dark energy inside that initially is formed by conversion from normal matter, has to be proposed.

 

[Ken G]

Not the initial appearance of dark energy, no; that happens, as I said, as some kind of phase transition inside the collapsing matter when it first collapses. That initial appearance of dark energy is what enables the claimed coupling with expansion to work.

But none of that is claimed in the article in the OP. All that is claimed, observationally, is that the mass of the black hole couples to the expansion, so the mass rises slowly as the expansion proceeds. That, in turn, is used to explain the acceleration, as the mass rises in just such a way as to be proportional to the volume of the universe, which is what you need to get a cosmological-constant-like acceleration.

It is true that several black hole models are mentioned to try to justify why that mass increase could happen, but there are not any models yet that really work this way (that combine the spin that black holes must have, and the "observed" mass increase, and accelerated boundary conditions). There is also not any speculation about the nature of the dark energy, or if a phase change of some kind occurs, or when it occurs. I understand that you are adding interpretational elements that seem necessary for this all to hang together, but I don't see why you claim that something has to happen to the mass as it enters in order to make this work. It seems to me, all one needs is a coupling between the black hole mass and the acceleration, and how that coupling occurs is unspecified and unknown, until a theoretical model is produced that actually does this (and with pure GR, if possible). In other words, it is observational guidance for motivating theory, but the nature of that theory is not yet established, other than that it is (hopefully) supposed to come from pure GR and nothing else. I'm not sure that some kind of dark energy phase change would actually qualify as pure GR, and I don't say that something like that might eventually be needed (as you seem to anticipate, no doubt because of a deeper understanding of what GR is and is not capable of), but it's unspecified in the current picture (and would probably disappoint the authors if true, as they are hoping it can be done with pure GR).

Once the initial dark energy is there (having been converted from the ordinary matter that collapsed), it then increases over time as a result of the claimed coupling with expansion. At least, that's my understanding of the model being proposed.

And that is indeed the issue. They need the mass to increase, and they need that mass increase to be proportional to volume of the universe (which is what they claim to observe), in order for it to act like dark energy. Whether there really is anything in their model that looks any different from the mass of the black hole is not specified, and I believe the authors hope will prove unnecessary. That's why this is not really an attempt to explain dark energy, so much as an attempt to do away with dark energy. If they fail to do away with dark energy, then they have simply moved the goalposts, and that is not their goal.

As far as I can tell, the claimed coupling is just to the expansion, not to acceleration.

Yes, it's to the expansion, but the article claims that it is important that the expansion is accelerated. Acceleration is what you get with the k=3 type of coupling they claim to observe, since if k=3, the increased mass is proportional to universal volume, so acts like dark energy, so produces the observed acceleration in an internally self-consistent way. If k is not 3, then the acceleration might still fit what is seen, but only because the expansion is not perfectly well constrained observationally. But it would not be cosmological-constant-like, so would not have the same effect as what is normally meant by "dark energy." (Though of course, that term could also be used to mean anything we don't yet understand, it just doesn't usually mean that.)

No, it can't, because there is nothing inside an ordinary black hole that does this. That's why a different model of what these objects actually are, with dark energy inside that initially is formed by conversion from normal matter, has to be proposed.

It depends on what you mean by an "ordinary black hole." I believe you mean that the common solutions ordinarily chosen, but those are called "provisional" in the paper, because they have incorrect boundary conditions at infinity. So they are looking for a different kind of "ordinary black hole", one that is ordinary in the sense that it is pure GR, and has the correct boundary condition. However, no such solution yet exists, so they are hoping to lead to the discovery of a solution like that-- which would immediately redefine the meaning of "ordinary." I believe you are expressing skepticism that this will prove possible, you think it will at some point be necessary to imbue these black holes with some new attributes that will look like a phase change into dark energy. That would simply move the goalposts though-- it would mean instead of asking what is happening in space that looks like an energy, we'd be asking what is happening in black holes that couples to expansion. That really wouldn't improve the situation much if it turns out to survive future tests, in fact we'd then wish we could go back to saying that space contains energy, that seemed closer to being explainable (after all, we were only off by 120 orders of magnitude)!

 

[PeterDonis]

none of that is claimed in the article in the OP

Sure it is; they reference singularity-free BH models and various papers that discuss them. Those models all have dark energy inside--that's the only way to get a singularity free model. But, as I have already pointed out, ordinary matter, which is what collapses to form BHs in the first place is not dark energy, so the dark energy has to form by some sort of phase transition during the collapse process. Various papers discussing the singularity free models differ in how much they discuss this fact, but that doesn't make it any less a fact.

All that is claimed, observationally, is that the mass of the black hole couples to the expansion, so the mass rises slowly as the expansion proceeds.

That's the observational claim that is used to focus on a particular class of BH models, yes. But the overall claim of the paper depends on those models, not just on the observations.

there are not any models yet that really work this way (that combine the spin that black holes must have, and the "observed" mass increase, and accelerated boundary conditions).

I'm not sure the authors of the paper would agree with this.

There is also not any speculation about the nature of the dark energy, or if a phase change of some kind occurs, or when it occurs.

This particular paper does not go into such things itself; it references other papers that do. See above. The paper does take it as given that BH models with dark energy inside are required; for example, on p. 3 it says "Vacuum energy interior solutions with cosmological boundaries have been predicted to produce" the coupling value that the paper claims to see in the observational data.

I don't see why you claim that something has to happen to the mass as it enters in order to make this work

Because for a singularity free BH solution you need dark energy, and for accelerating expansion you need a dark energy equation of state. But, as noted above, ordinary matter, which is what collapses to form BHs, is not dark energy. It has the wrong equation of state. So there must be a phase transition of some kind that changes the equation of state inside these objects.

They need the mass to increase, and they need that mass increase to be proportional to volume of the universe (which is what they claim to observe), in order for it to act like dark energy.

No, that alone is not sufficient to "act like dark energy". You also need a dark energy equation of state. That involves the pressure, not just the mass density.

the article claims that it is important that the expansion is accelerated

That's because they accept that observations show that the expansion is accelerated. They are taking that as a given, and adding to it their observational claim about masses of BHs coupling to the expansion, in order to account for the accelerated expansion.

It depends on what you mean by an "ordinary black hole."

I mean a black hole solution in which ordinary matter collapses, and because it's ordinary matter and no phase transition occurs, the singularity theorems guarantee that there will be a singularity inside.

Note that this does not require the solution to be asymptotically flat; there is a singularity in the Schwarzschild-de Sitter solution, for example, which is a Schwarzschild BH with a de Sitter boundary, not an asymptotically flat boundary. (I'm not sure the authors of the paper fully realize this.)

they are looking for a different kind of "ordinary black hole", one that is ordinary in the sense that it is pure GR

What does "pure GR" mean? Dark energy is perfectly within the scope of GR.

and has the correct boundary condition. However, no such solution yet exists

The authors of the paper might believe this, but they are wrong. The Schwarzschild-de Sitter solution is such a solution. See above. There is also a Kerr-de Sitter solution if one wants a more realistic hole with spin.

 

[artis]

Up to now, it was assumed that dark energy was also uniform, not clumped, so nobody ever had to ask whether "clumps" of dark energy would average. But with this proposed model, that question now becomes relevant and would need to be answered. The proposed model doesn't answer it as far as I can see; it just assumes that the averaging works. It's possible that there is a simple answer somewhere, but I have not seen one.

Well that was my point, because clearly the dark energy within the black holes is clumped or one could say much denser than in the surrounding empty space and I say empty space because ordinary matter doesn't have dark energy nor it influences dark energy.
So you essentially have a dark energy distribution throughout space with "hot spots" or places where that energy is stronger.
I don't know truth be told but I would think black holes on average are less in count and further spaced apart than ordinary matter made objects like planets, stars and cosmic dust clouds so i would imagine that the energy distribution of dark energy (if this paper is true ) could not be as uniform over large scale as the gravitational pull from ordinary matter. This then should have an impact on the homogeneity of the expansion would it not?
What are your thoughts ?

 

[artis]

Ok so to recap to keep track of everything.

1) It is proposed that ordinary matter within SMBH turns into dark energy by some unknown mechanism
2) Dark energy exists both within such black holes as well as outside
3) Dark energy within such black holes couples to the one already existing outside and result in the overall expansion of space
4) Because dark energy is inside such black holes and there it is more dense than outside - this allows the black hole to gain mass/energy even without the accretion of matter.

5) The authors argue that any given SMBH grows proportionally to the overall dark energy expansion ratio of space and it's own black energy content, so a black hole with less mass would have less dark energy and it's growth over that which it could attain on ordinary matter only would also be less than for another black hole that started out with more matter?
Either way I have to agree with @Ken G that I'm not sure how much this new theory resolves. I would say the main problem is we are still not an inch closer to understanding what dark energy really is.

One mystical side of this to me is - why does dark energy exist both within as well as outside of black holes , because clearly the conditions are different inside VS outside.

@PeterDonis you claimed that BH don't radiate this dark energy so basically we have a proposed mechanism of ordinary matter creating dark energy inside a black hole but then what creates dark energy outside a black hole?

Doesn't this new paper have to then come up with basically two different mechanism of how dark energy is created because it seems to me that the process (whatever it is, who knows honestly) that creates this energy within a BH is not the same that creates it within the rest of empty space?

 

[JLowe]

I don't know truth be told but I would think black holes on average are less in count and further spaced apart than ordinary matter made objects like planets, stars and cosmic dust clouds so i would imagine that the energy distribution of dark energy (if this paper is true ) could not be as uniform over large scale as the gravitational pull from ordinary matter. This then should have an impact on the homogeneity of the expansion would it not?
What are your thoughts ?

I don't know, how much does that actually matter at the ridiculous distances being discussed. The distance from us to some galaxy receding away from us is practically the same for its black holes or its ordinary matter. Most of the matter seems to be clumped in essentially the same places we find black holes given such large scales.

At smaller scales, the difference is more significant, but then at smaller scales, such as some arbitrary volume of our own galaxy, we don't really see expansion at all, only gravitationally bound systems.

But this is all above my pay grade, so I don't pretend to fully understand it.

 

[Bandersnatch]

The authors of the paper might believe this, but they are wrong. The Schwarzschild-de Sitter solution is such a solution. See above. There is also a Kerr-de Sitter solution if one wants a more realistic hole with spin.

I don't think they don't realise that. From section 4.6:

As described in §1, there are known exact solutions with each of the following properties: strong spin, arbitrary RW asymptotics, dynamical mass, and interior vacuum energy equation of state. Our result implies the existence, within GR, of an exact solution with all of these properties. Currently, there is no known solution that possesses all four, though there are known solutions with various combinations of two.

 

[Ken G]

Sure it is; they reference singularity-free BH models and various papers that discuss them. Those models all have dark energy inside--that's the only way to get a singularity free model. But, as I have already pointed out, ordinary matter, which is what collapses to form BHs in the first place is not dark energy, so the dark energy has to form by some sort of phase transition during the collapse process. Various papers discussing the singularity free models differ in how much they discuss this fact, but that doesn't make it any less a fact.

I see your point, black holes with vacuum energy interiors are an attractive way to get k=3, and that does seem to be what they have in mind. Since they don't form from vacuum energy, some kind of transition is required in there. So the issue of vacuum energy is not actually removed or resolved, merely confined to within black holes. It's a bit like intentionally leaving the keys somewhere out of the streetlight, which would be unattractive except that they feel k=3 has some theoretical attractiveness. Then by removing vacuum energy from the rest of the universe, they are saying it would have to be something that is only possible due to the kind of phase change you are talking about.

That's the observational claim that is used to focus on a particular class of BH models, yes. But the overall claim of the paper depends on those models, not just on the observations.

The claims are certainly inspired by those models, though the actual results of the paper do not need to even mention models. They claim to have a result that gets k=3 without knowing any GR at all, though we all agree the observations require corroboration because others have looked at this kind of data without it jumping out at them that black holes have gained an order of magnitude in mass in galaxies experiencing little accretion.

I'm not sure the authors of the paper would agree with this.

I got it straight from the paper:
"As described in Section 1, there are known exact solutions with each of the following properties: strong spin, arbitrary RW asymptotics, dynamical mass, and interior vacuum energy equation of state. Our result implies the existence, within GR, of an exact solution with all of these properties. Currently, there is no known solution that possesses all four, though there are known solutions with various combinations of two (e.g., Guariento et al. 2012; Dymnikova & Galaktionov 2016). Finding solutions that feature all four properties is an important theoretical step forward."
So their perspective is they have an observational result that is intended to stimulate a GR solution that does not yet exist.

This particular paper does not go into such things itself; it references other papers that do. See above. The paper does take it as given that BH models with dark energy inside are required; for example, on p. 3 it says "Vacuum energy interior solutions with cosmological boundaries have been predicted to produce" the coupling value that the paper claims to see in the observational data.

Yes, you are right that they very much are picturing black holes with vacuum energy interiors, as part of the interpretation of their observational results that do not, by themselves, require that to be the case. So although it might turn out that black holes have k=3 for other reasons than internal dark energy, that is not what is currently expected, and you are justified in focusing on that situation.

No, that alone is not sufficient to "act like dark energy". You also need a dark energy equation of state. That involves the pressure, not just the mass density.

The way this has always been explained to me is that a general way to think about pressure is the negative of the energy change per volume change. Hence anything that attributes energy in proportion to volume is going to have negative pressure, and produce the gravitational consequences of that. If the vacuum everywhere in the universe has a constant energy density, then energy is proportional to volume, but you get the same effect if you have a discrete set of black holes that are increasing in energy (increasing their mass-energy) proportional to the volume increase, it works the same way to produce a negative gravitational pressure. So you get the necessary equation of state automatically. Perhaps I am wrong that just increasing the mass would do that, but it only seems to require associating energy with the black hole mass.

That's because they accept that observations show that the expansion is accelerated. They are taking that as a given, and adding to it their observational claim about masses of BHs coupling to the expansion, in order to account for the accelerated expansion.

Yes, I agree.

I mean a black hole solution in which ordinary matter collapses, and because it's ordinary matter and no phase transition occurs, the singularity theorems guarantee that there will be a singularity inside.

Right, that is the part I did not understand until now, thank you.

Note that this does not require the solution to be asymptotically flat; there is a singularity in the Schwarzschild-de Sitter solution, for example, which is a Schwarzschild BH with a de Sitter boundary, not an asymptotically flat boundary. (I'm not sure the authors of the paper fully realize this.)

It might be the issue of spin. They realize that kind of thing is possible, but they expect black holes to spin, so they think something is missing.

What does "pure GR" mean? Dark energy is perfectly within the scope of GR.

Yes, they still need dark energy, they just need it inside the black hole, which they are hoping will turn out to be something that emerges naturally from the necessary black hole solution. But it could be argued that without black holes, we already had dark energy emerging as a solution to the accelerated expansion, so I was wrong they they are trying to circumvent that completely. Instead, they think it is a step forward to just quarantine it to within black holes. It's not so obvious that really is much of a step forward, but they can always argue that we have no choice, if k really turns out to be 3.

The authors of the paper might believe this, but they are wrong. The Schwarzschild-de Sitter solution is such a solution. See above. There is also a Kerr-de Sitter solution if one wants a more realistic hole with spin.

That last point seems to be the key issue, they don't think it has been done with strong spin in a way that has the black hole mass increase with k=3. So they are saying, they think their observations require k=3 (many are not yet convinced), so any solution that doesn't have that property will be found wanting, and other solutions must still be sought.

 

[Ken G]

Ok so to recap to keep track of everything.

1) It is proposed that ordinary matter within SMBH turns into dark energy by some unknown mechanism

All black holes. They can only observe it happening in SMBHs, but they also need it to happen in stellar-mass black holes in order to work like a cosmological constant (most black hole mass is in small BHs, not SMBHs).

2) Dark energy exists both within such black holes as well as outside

It won't need to be outside any more-- maybe it still contributes out there, but it isn't needed any more.

3) Dark energy within such black holes couples to the one already existing outside and result in the overall expansion of space

They don't need it to couple to the dark energy outside, they can couple it directly to the expansion without any dark energy outside.

4) Because dark energy is inside such black holes and there it is more dense than outside - this allows the black hole to gain mass/energy even without the accretion of matter.

It probably depends on the nature of the GR solution they are seeking that does not yet exist, as to what is the "because" behind the coupling.

5) The authors argue that any given SMBH grows proportionally to the overall dark energy expansion ratio of space and it's own black energy content, so a black hole with less mass would have less dark energy and it's growth over that which it could attain on ordinary matter only would also be less than for another black hole that started out with more matter?

They don't say anything about the accretion of ordinary matter, they are looking at black holes that they hope are not really accreting much. Black holes that are accreting would just add that on, as that matter gets converted into dark energy like PeterDonis has been saying, and then participates in the coupling.

Either way I have to agree with @Ken G that I'm not sure how much this new theory resolves. I would say the main problem is we are still not an inch closer to understanding what dark energy really is.

Yes, I was incorrect that their picture can allow us to eliminate dark energy altogether, it just quarantines it into black holes. If you like putting what you don't know someplace you can't see, then that's a good thing, but if that feels like a cheat, then it isn't.

One mystical side of this to me is - why does dark energy exist both within as well as outside of black holes , because clearly the conditions are different inside VS outside.

PeterDonis can correct me, but I don't think they need dark energy anywhere except inside black holes. So there could be something about the extreme properties of black-hole spacetime that allows the creation of dark energy. Of course, extreme conditions also existed in the early Big Bang, so why not create it there as well. It's not really much of an advance, unless it provides insight into how such extreme conditions work.

 

[Ken G]

Another point to bear in mind here is that SMBHs with 10^10 solar masses have been observed at z=10 or so, and if k=3, those SMBHs will have 10^13 solar masses today. That is more massive than a whole galaxy, so their picture requires that these monsters must be so few and far between that we are too far from any of them to be able to see them now. The paper also alludes to some idea that black holes with mass larger than 10^11 are hard to see, perhaps they just suck everything in before it has much of a chance to radiate, so there might be monster black holes around that are invisible. They also say that stellar-mass black holes that have gained in mass in the Milky Way halo are not ruled out by MACHO searches. But still, that would mean lots of black holes that have much more mass than a stellar-mass black hole is supposed to get. It has been a puzzle how there could be "intermediate" mass black holes, and how gravitational waves could come from stellar-mass black holes, but I'm wondering if this new idea would create an "embarrassment of riches"-- way too many intermediate mass black holes, and way too many gravitational wave sources. The authors address that in section 4.5, but it seems like a potential problem.

 

[phinds]

The paper also alludes to some idea that black holes with mass larger than 10^11 are hard to see, perhaps they just suck everything in before it has much of a chance to radiate, so there might be monster black holes around that are invisible.

Would not such monsters create Einstein Rings that would be visible even at long distance?

 

[Ken G]

Would not such monsters create Einstein Rings that would be visible even at long distance?

You can't see long distance and also see low z. Long distance means higher z, so the monsters aren't quite so monstrous yet. What you're saying is true, but one has to look at just what volume is accessible there. There might be either a "smoking gun" that the idea is true, or a fatal flaw that it can't be, and the authors must be waiting for the other shoe to drop.

 

[PAllen]

One criticism I've heard from some physicists (but I don't see it published yet) is that black holes observed gravitational mass is much less than 1% of total mass per large cosmological volume. Dark Energy equation of state means pressure is the negative of gravitational mass, but it doesn't change the mass. Yet, in terms of mass, dark energy is required to be around 70% of total mass/energy over large cosmological volumes. How do black holes (with less than 1% observed mass) possibly account for this?

 

[PeterDonis]

I would think black holes on average are less in count and further spaced apart than ordinary matter made objects like planets, stars and cosmic dust clouds

I'm not sure what you're basing this on. I don't think we can infer this from the data we have.

 

[PeterDonis]

From section 4.6

Hm. Of course their "requirements" are driven by their particular hypothesis. Only one of them, strong spin, is observationally supported (if we put aside the observational claims in this paper itself). "Arbitrary RW asymptotics" is not actually necessary, because you can always "glue" together spacetime regions with different metrics. "Interior vacuum energy equation of state" is nice because it provides singularity-free solutions, but by itself it doesn't give what the paper is claiming. The key requirement for the paper's claim is "dynamical mass", and that is the most questionable one. How does this "dynamical mass" work without violating the condition that the covariant divergence of the stress-energy tensor must be zero?

 

[PeterDonis]

1) It is proposed that ordinary matter within SMBH turns into dark energy by some unknown mechanism

Yes.

2) Dark energy exists both within such black holes as well as outside

Not according to the paper. The paper proposes a model in which there is no dark energy outside of the exotic collapsed objects.

3) Dark energy within such black holes couples to the one already existing outside and result in the overall expansion of space

No. The "coupling" is the paper's hypothesis for how the dark energy inside the exotic collapsed objects can increase with time once such objects are formed. It has nothing to do with any coupling to dark energy outside the objects, since in the paper's hypothesis there is none (see above).

4) Because dark energy is inside such black holes and there it is more dense than outside - this allows the black hole to gain mass/energy even without the accretion of matter.

No. See above.

 

[PeterDonis]

5) The authors argue that any given SMBH grows proportionally to the overall dark energy expansion ratio of space and it's own black energy content

No. The rate of growth is the expansion rate of the universe (just the expansion rate, nothing to do with "dark energy expansion ratio", whatever that is) times a coupling constant $k$ that depends on the type of stress-energy inside the SMBH. The paper claims that their hypothesized dark energy inside these SMBHs gives a $k$ of about 3, which is what they claim is necessary to explain the observed accelerated expansion of the universe.

 

[Ibix]

3) Dark energy within such black holes couples to the one already existing outside and result in the overall expansion of space

Remember that space expands in all FLRW models, whether there's dark energy or not. Dark energy simply adjusts the rate of expansion. The claim seems to be that if you put a black hole into an FLRW spacetime and handle the behaviour at infinity correctly (with the paper's definition of "correctly" ) then the black hole masses grow as they are coupled to the expansion somehow.

 

[Ken G]

One criticism I've heard from some physicists (but I don't see it published yet) is that black holes observed gravitational mass is much less than 1% of total mass per large cosmological volume. Dark Energy equation of state means pressure is the negative of gravitational mass, but it doesn't change the mass. Yet, in terms of mass, dark energy is required to be around 70% of total mass/energy over large cosmological volumes. How do black holes (with less than 1% observed mass) possibly account for this?

I believe their claim is that the black hole mass rises greatly, so that it is 70%, so the observation of 1% is falsely interpreted because it doesn't allow the black holes to keep growing in mass "after we see them." (After all, they do calculate the self-consistent cosmological constant that stems from their model.)

 

[PeterDonis]

by removing vacuum energy from the rest of the universe, they are saying it would have to be something that is only possible due to the kind of phase change you are talking about.

Yes.

anything that attributes energy in proportion to volume is going to have negative pressure

No, this is not correct. You need an actual form of stress-energy that has the equation of state $p = - \rho$. Having energy be proportional to volume by itself is not enough; lots of ordinary matter meets that condition to a good approximation.

 

[PAllen]

I believe their claim is that the black hole mass rises greatly, so that it is 70%, so the observation of 1% is falsely interpreted because it doesn't allow the black holes to keep growing in mass "after we see them."

That does not make sense to me. For a region of substantial size 'near' us, we are seeing 'near' current mass of BH. While high z BH are seen as they were in the past, if their present is radically different from the region around us, then homogeneity is violated, and the framework of FLRW models is broken.

 

[artis]

I would think black holes on average are less in count and further spaced apart than ordinary matter made objects like planets, stars and cosmic dust clouds

I'm not sure what you're basing this on. I don't think we can infer this from the data we have.

black holes observed gravitational mass is much less than 1% of total mass per large cosmological volume.

 

[artis]

No. The "coupling" is the paper's hypothesis for how the dark energy inside the exotic collapsed objects can increase with time once such objects are formed. It has nothing to do with any coupling to dark energy outside the objects, since in the paper's hypothesis there is none (see above).

Ok , thanks for the correction I think I now see the picture of why @Ken G complained about "bootstrapping"

So ordinary matter falls into a BH there it turns into dark energy which then drives the expansion of space but only from within black holes and as the space expands the black holes expand with it thereby also increasing the dark energy content within the hole itself thereby again giving a positive feedback on the expansion of space?

 

[PeterDonis]

So ordinary matter falls into a BH there it turns into dark energy which then drives the expansion of space but only from within black holes and as the space expands the black holes expand with it thereby also increasing the dark energy content within the hole itself thereby again giving a positive feedback on the expansion of space?

That's the basic hypothesis of the paper, yes.

 

[PAllen]

Another criticism, also not yet published, is described in:



at around 20 minutes through the end of the video. Smethurst's primary research is in BH growth, and she finds the data analysis wholly unconvincing (she would never make such an accusation, but what I feel from her discussion is an implicit accusation of cherry picking data to fit a hypothesis). I would summarize her conclusion as "beautiful idea, I don't believe a word of it". She hints that multiple rebuttal papers are forthcoming. Also, she gives a bit of history of ideas on the path to this paper, with links.

[edit: I request that we not focus on her mischaracterization of the nature of a Kerr BH singularity. I am quite sure she is just taking poetic license to avoid a sidetracking the main discussion with a presentation on singularity structure.]

 

[Ken G]

Yes.No, this is not correct. You need an actual form of stress-energy that has the equation of state $p = - \rho$. Having energy be proportional to volume by itself is not enough; lots of ordinary matter meets that condition to a good approximation.

I don't know what you mean by ordinary matter meeting the condition that the energy stays proportional to the volume of the universe as the universe expands. Of course I am not talking about a perfectly mundane lump of mass whose internal energy is proportional to its own volume, I'm talking about its energy being proportional to the volume of the universe (the cube of the scale parameter). That's what these black holes are said to do, so it's nothing like ordinary matter.

 

[PeterDonis]

I'm talking about its energy being proportional to the volume of the universe (the cube of the scale parameter). That's what these black holes are said to do, so it's nothing like ordinary matter.

I agree, but that's not the claim you made earlier that I objected to. You claimed that just having energy being proportional to volume, all by itself, makes something have the same gravitational effect as dark energy. That's wrong; it doesn't. You need an actual substance--stress-energy--that has the dark energy equation of state $p = - \rho$, where $\rho$ is the total energy density. (Strictly speaking, any equation of state for which $p < - \rho / 3$ will lead to some amount of accelerated expansion, but for the kind of accelerated expansion we observe, something at least very close to $p = - \rho$ would be required.) You can't magically make something have that equation of state just by stipulating that its total energy grows like the scale factor of the universe cubed. (Nor do I think the paper itself is making that claim; they are saying the stress-energy inside these objects is dark energy independent of the "coupling" hypothesis about how it grows with expansion.)

(As I pointed out in an earlier post, I'm skeptical that this kind of energy growth can happen without violating the requirement that the covariant divergence of the stress-energy tensor is zero. But that's a separate issue from the above.)

 

[Ken G]

Another criticism, also not yet published, is described in:



at around 20 minutes through the end of the video. Smethurst's primary research is in BH growth, and she finds the data analysis wholly unconvincing (she would never make such an accusation, but what I feel from her discussion is an implicit accusation of cherry picking data to fit a hypothesis). I would summarize her conclusion as "beautiful idea, I don't believe a word of it". She hints that multiple rebuttal papers are forthcoming. Also, she gives a bit of history of ideas on the path to this paper, with links.

[edit: I request that we not focus on her mischaracterization of the nature of a Kerr BH singularity. I am quite sure she is just taking poetic license to avoid a sidetracking the main discussion with a presentation on singularity structure.]

Thanks for the link. She is saying that if the data shows more recently formed ellipticals have higher-mass SMBHs, it is probably because they were formed from more mature disk galaxies that accreted more mass into their own SMBHs prior to merger, so we are really seeing a trend that ellipticals that form at low z have much more massive SMBHs essentially because they had more time to build them up prior to the merger that made the elliptical. But what I don't understand about that argument is that it seems to assume an elliptical we see at z=1 is formed at z=1 also, so that when we compare it to one seen at z=2, it is more recently formed. Why could we not have a lot of z=1 ellipticals that formed at z=2 and really haven't done anything since, so have not taken advantage of all that mature-disk accretion she is suspicious of? It doesn't seem to be a killing criticism, until we know the fraction of z=1 ellipticals that have actually been around for a long time prior to that.

Regardless of how that particular criticism plays out, the real problem might be that Farrah et al. have presented their results as evidence for coupling (with their unfortunate claim that zero coupling is ruled out to 99.98% confidence, that's obviously a statistical statement that is ignoring systematic errors which would of course be the real challenge to "confidence"), rather than simply saying their result could have ruled out z=3 coupling but didn't. No doubt they wanted to make a splash, but they have opened themselves up to rebuttal about the reliability of their evidence, where they could have avoided that by simply saying their evidence is consistent with coupling, and is only inconsistent with no coupling if they have not introduced systematic error into their interpretation (which is certainly way more than 0.02% likely).

 

[Ken G]

You can't magically make something have that equation of state just by stipulating that its total energy grows like the scale factor of the universe cubed. (Nor do I think the paper itself is making that claim; they are saying the stress-energy inside these objects is dark energy independent of the "coupling" hypothesis about how it grows with expansion.)

Yes, they do seem to feel you need P = -rho inside the black holes to make this work, so I accept your initial statements that at some point you need to convert to dark energy inside these black holes to make this idea fly. So perhaps their argument could be framed that empirical evidence for k=3 can be taken as evidence in favor of a P = -rho type of EOS inside black holes.

(As I pointed out in an earlier post, I'm skeptical that this kind of energy growth can happen without violating the requirement that the covariant divergence of the stress-energy tensor is zero. But that's a separate issue from the above.)

The video by Smethurst talks about growing the energy of the black hole at the expense of "diluting" the spacetime around it, which sounds like one can get some kind of averaged zero divergence by including both those effects, but all this seems very boiled-down to plain language so it will have to await the kind of formal analysis you are talking about.

 

[PeterDonis]

some kind of averaged zero divergence

The covariant divergence law is not an averaged law. It has to hold exactly at every single event in spacetime.