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

[Bandersnatch]

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?

Isn't that where the 'therefore acts as dark energy' bit comes from? From the paper:

When accretion becomes subdominant to growth by cosmological coupling, this population of BHs will contribute in aggregate as a nearly cosmologically constant energy density.
From conservation of stress-energy, this is only possible if the BHs also contribute cosmological pressure equal to the negative of their energy density, making k ∼ 3 BHs a cosmological dark energy species.

Later on, they cite Croker et al. 2020 for that (and both refer to Gliner 1966 as seminal). Perhaps criticism of whether the theory is correct should be aimed at those papers?I'd like to note for the discussion, that the specific claim the paper makes is not that BHs (or, what we tend to think of as black holes) >can< grow with expansion or act as DE - these are taken as given, to claim that BHs with these properties are consistent with the two kinds of observational data shown in the paper. I.e., they are saying something along the lines of 'maybe we should take these particular models more seriously because it kinda fits?'
This is observational astronomy, not theory development. They work out very little in terms of new ideas in the paper. It 'merely' attempts to tie together earlier work into a new picture.

 

[Ken G]

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

OK, so it needs to connect the globally averaged concept of a growing mass and a "diluting" spacetime (as per Dr. Smethurst's way of thinking about it), with certain formal requirements for it to work in GR. We'll have to see if a solution with all the desired properties is really possible, that might be a useful outcome of this paper even if the observational interpretation is found wanting. After all, flaws in the interpretation don't make the idea wrong, they only make it unsupported.

 

[PeterDonis]

Isn't that where the 'therefore acts as dark energy' bit comes from?

The claim you quote is more than just "dynamical mass"; it's the claim that the global behavior of a population of such objects is the same as that of a constant dark energy density. Which, as I said before, means that not just the mass (or energy density) but the pressure has to average globally to the same equation of state that the individual objects have.

Perhaps criticism of whether the theory is correct should be aimed at those papers?

That would be one good area to focus on, yes. They basically seem to be reasoning backwards: that since the covariant divergence of the stress-energy has to be zero, somehow their "coupling" process has to obey that law, even though they have no idea how. That seems like an obvious weak point in the argument.

 

[Ken G]

Perhaps the real source of dark energy is.... wishful thinking?

 

[artis]

Perhaps the real source of dark energy is.... wishful thinking?

That definitely has a non zero coupling constant to the expansion of databases like arxiv.
Since the digital age that expansion has been accelerating...

 

[elcaro]

Exactly what I am puzzled by

One explenation would be that dark energy forms in the interior of the collapsing star before it becomes (or never becomes) a black hole.... Could that be correct?
And the follow up question is how this process would create more energy as E=mc^2 allows...

 

[martinbn]

Sorry if I repeat someone, but here are some thoughts by Ethan

 

[Ken G]

That blog post is certainly very useful and informative, but as a critique of the paper, it's actually quite thin. It does not contribute any evidence as to the validity or invalidity of the observational technique (presumably because his area is theory), it just points out something that the authors already point out in their paper: the rise in black hole mass could be either from normal accretion, or from cosmological coupling. Then he says he thinks it's more likely the former than the latter-- without giving any reason at all for that belief of his! If I'm an author, and I'm looking at Ethan's post, my reaction would be "everything you said I already knew before I analyzed the data, but he data convinced me of the latter possibility. I guess everyone is entitled to their opinion." And that's it, the post gives no reason to believe one or the other hypothesis, it is pure opinion without citing any new evidence at all.

Indeed, Siegel is even a bit disingenuous here. He lists three reasons why no one was thinking about black holes as part of the overall expansion, and they were:

• For one, we can quantify how much gravitational binding energy there is in black holes, and it’s only about 0.01% of the needed amount of energy to explain dark energy.
• For another, the dark energy density needs to remain constant over time, but the number density and mass density of black holes decreases over time, especially at very late times.
• And for yet another, individual black holes actually grow over time and new black holes continuously form, but this growth occurs much more slowly than the rate at which the Universe expands.

So yes, those are good reasons for people to rule out black holes as being cosmologically important-- unless there's cosmological coupling. He kind of leaves out that crucial caveat! If I'm an author, and reading that, I'm actually a bit miffed at this point, because he makes it sound like those are three reasons to rule out cosmological coupling, when in fact those three reasons are the whole point of why cosmological coupling could make black holes cosmologically important! It's easy to see how cosmological coupling provides an alternative to all three of those objections to the importance of black holes. And here's the disingenuous part: if Siegel's hunch is right and the black-hole mass increase is due to normal accretion, then that already invalidates the first bullet above, because k=3 mass increases in black holes make their mass way more important cosmologically-- you just don't get the acceleration if it isn't dark energy (as per what PeterDonis has been telling us). The black holes would have to be eating up a significant chunk of the mass in the universe to grow that fast by accretion!

Now, none of that makes Siegel wrong, but also, none it makes the authors wrong. It's an observational issue now, to corroborate or refute their conclusions, and it is a theoretical issue to seek the missing GR solution they have all mentioned. I just don't see the point in putting odds on how all that will turn out-- if you have nothing to say about potential observational flaws, or potential sticking points in the hoped-for GR solution, then you don't really have much to add to the question. That said, I do appreciate all the useful information he presented, and he has every right to include his opinion, it's just not a critique of the paper.

I feel he would have been on stronger ground had he simply said their claim that the absence of cosmological coupling is ruled out to 99.98% confidence overlooks the significant possibility that their observed effect is due to something else (like normal accretion). I think we can all agree that chance is much much larger than 0.02% ! But when Siegel put odds on them being right, that was just personal opinion, not really a valid critique. It's "argument by authority" rather than "argument by evidence."

And here's the thing no one seems to be noticing: If the BH mass rise is due to normal accretion processes, then why k=3? Coincidence, apparently? My guess is, this "why 3" issue is what convinced the authors.

 

[.Scott]

I mentioned this before, but let me explicitly ask: In the paper, there is a "scaling term" that goes along with that coupling exponent "k" (k is about 3). It seems to me that it should have been easy for them to report the value of that scaling term ($a_i$). Could anyone tell me what the approximate value of $a_i$ is? Or does it require observation data that is not included in the paper?

 

[Bandersnatch]

$a_i$ is the scale factor $a$ at the time a particular object was formed. It doesn't have a single value.

 

[.Scott]

$a_i$ is the scale factor $a$ at the time a particular object was formed. It doesn't have a single value.

So it's the just the mass of a particular BH at a particular start time - or tied to such a value.

 

[Ibix]

So it's the just the mass of a particular BH at a particular start time - or tied to such a value.

No, it's the scale factor of the universe at the formation of the black hole - so $a/a_i$ is the ratio of distance between a pair of comoving galaxies now and the distance between them when the hole formed.

 

[ohwilleke]

Relevant.

The hypothesis that the mass of BHs increases with time according to the same law as the volume of the part of the Universe containing it and therefore the population of BHs is similar to dark energy in its action was recently proposed. We demonstrate the reasons why it cannot be accepted, even if all the assumptions on which this hypothesis is based are considered true.

S L Parnovsky, "Can black holes be a source of dark energy?" arXiv:2302.13333 (February 26, 2023).

 

[Bandersnatch]

As far as rebuttals go, that one is a poor effort. All it says (and I mean >all<, in almost this many words) is:
1. but black holes are not repulsive!
2. even if they were, that would make things fall apart instead of fall in, and we see things falling in

I kinda feel it misses the point.

 

[PeterDonis]

As far as rebuttals go, that one is a poor effort. All it says (and I mean >all<, in almost this many words) is:
1. but black holes are not repulsive!
2. even if they were, that would make things fall apart instead of fall in, and we see things falling in

I kinda feel it misses the point.

I don't think so. The key criticism is here (p. 4, start of third paragraph down): "The black hole system does not have negative pressure". Notice that they say "system"--they are not talking about the individual objects themselves, they are talking about a system composed of a huge number of them, and asking how we would model this system as a whole.

Here is how I would restate this key criticism: if we have a collection of many "black hole" objects that have dark energy inside, so that in the interior of each black hole, the equation of state is $p = - \rho$, that does not mean that the equation of state of the system as a whole, considered as a "fluid" of which the individual "black hole" objects are the "particles", has the equation of state $p = - \rho$. In fact, if the objects appear from the outside the same as ordinary black holes--things fall into them--then the standard way to treat a "fluid" composed of many such objects would be as cold ordinary matter, with $p = 0$.

The papers that make the claims about "coupling" of the masses of these objects to expansion, and attempt to account for accelerated expansion in this way, give no argument for why the equation of state of the "fluid" composed of a huge number of these objects should be $p = - \rho$. They simply assume it without proof or argument. This paper is simply pointing out that that won't do: they need to actually show that the equation of state for the system as a whole will be that. Just saying "dark energy inside each object" isn't enough. The paper then gives reasons for being skeptical that any such showing can actually be made.

 

[Ken G]

I feel the missing element has to have something to do with how the coupling works to increase mass. Imagine we had a flow of black holes toward a central point for some reason. Then imagine we also had an expansion of the universe, such that the density of these inflowing black holes stayed constant. That sounds like a situation where you could have the mass density of black holes staying the same, but I doubt it would work like dark energy to induce an acceleration into the expansion, because the density was only being kept constant by moving mass in from elsewhere, so that by itself has consequences for the spacetime dynamics.

However, if there was no motion of the black holes, so they comoved with the expansion, yet their mass density was held fixed by a coupling that increased their mass with time, it sounds like this could be a very different situation because nothing is moving across any comoving boundaries. I'm not hearing in this article where those two situations are being distinguished, and I feel they must have very different consequences for the self-consistent expansion.

Related to this is the usual informal explanation of why "dark energy" has an equation of state like P ~ -rho. I realize this is not formal GR, but the standard motivation is that a general way to think about pressure is how the energy content inside a volume changes when the volume changes, P = - dU/dV. Note the key point: the change in energy content is not due to motion through the boundary of the volume, it is due to the change in volume itself. It is an intrinsic U change, not an advective U change. We still have two ways to make U = rho*V, we could move energy into the volume in proportion to how V grows, but that would not produce a negative pressure. However, if the physics inside the volume itself automatically has U rise like rho*V any time V changed, inherently to the V change, then P = -dU/dV does = -rho.

Of course the normal situation is that intrinsic changes in U due to V change (the classic example being expansion work done by gas pressure) cause a drop in U, not a rise, so we normally get positive pressure. The informal explanation of dark energy is that any time U is forced (intrinsically) to obey U = rho*V, then this intrinsic U change is positive as V rises, and that gives P = -rho. So that sounds a lot more like cosmological coupling to the black holes, than does simply keeping the mass density of black holes fixed in the "normal" way of moving them across boundaries. How does this paper distinguish between the various ways that the U/V is being held constant, and is it possible that their argument actually applies to advecting U across comoving boundaries but not coupling?

 

[elcaro]

I don't know if I understand this issue the way it is supposed to, but I hope someone can clarify. As I understand it this new finding relates the source of dark energy (aka cosmological constant - a postive energy desnity in combination with a negative pressure term) to a black hole. For an object to be a black hole it needs to have a horizon which causes the escape velocity of the dense and massive object to become light speed, so that nothing, not even light can escape it. Same is true for the gravitational field. The gravitational influence of the black hole for the stuff around is is still there because the curvature of space was already there before the horizon formed.

But here is my misunderstanding, I hope someone can clarify. If in the interior of a black hole for some reason the mass or energy changes, how could this affect spacetime outside the black hole horizon?
Or does this finding imply that the gravitational influece the interior mass/energy has on the spacetime outside the cosmological horizon can still propagate to the outside, ie. this kind of black hole is not really the text book black hole?

And as a follow up question, currently the universe contains 4% normal matter and around 68% dark energy. Does this finding imply that all of the dark energy was formed by normal matter in the interior of black holes, so it would have been much larger in the past?

 

[elcaro]

As far as rebuttals go, that one is a poor effort. All it says (and I mean >all<, in almost this many words) is:
1. but black holes are not repulsive!
2. even if they were, that would make things fall apart instead of fall in, and we see things falling in

I kinda feel it misses the point.

Same as the expansion of space (as how we thought it worked) does not cause gravitational bound objects to experience that expansion, so it was thought that the expansion of space only works in regions of space where there is no nearby source of gravity that could overcome the expansion of space. So the gravitational attraction of black holes simply overcomes the effects of space expansion, I assume.

 

[PeterDonis]

this new finding relates the source of dark energy (aka cosmological constant - a postive energy desnity in combination with a negative pressure term) to a black hole

Not to a black hole by the standard definition. The objects being called "black holes" in this context have no event horizons and no singularities. They look like black holes from the outside, but they only have apparent horizons, and the dark energy in their interiors prevents them from having singularities.

the gravitational influece the interior mass/energy has on the spacetime outside the cosmological horizon

A black hole horizon (meaning the event horizon of a standard black hole) is not the same as a cosmological horizon. The model proposed in the paper under discussion does not change anything about the cosmological horizon of our best current model of the universe.

this kind of black hole is not really the text book black hole?

That's correct. See above.

 

[PeterDonis]

currently the universe contains 4% normal matter and around 68% dark energy. Does this finding imply that all of the dark energy was formed by normal matter in the interior of black holes, so it would have been much larger in the past?

Yes. That's one of the reasons to be skeptical of the paper's claims, since there are multiple lines of evidence that indicate that it's highly unlikely that the ordinary matter content of our universe could have been as large in the past as it would have to be for the paper's proposed model to work.

 

[PeterDonis]

Just a speculation, and based on my limited understanding of how this speculated source of dark energy in the interior of black holes work.

Please don't speculate. The model proposed in the paper under discussion is already speculative. Piling speculation on speculation is extremely unlikely to be fruitful. The best we can do at this point is to try to identify additional pieces of evidence or theoretical analysis that would help to evaluate the paper's proposal.

 

[PeterDonis]

Same as the expansion of space (as how we thought it worked) does not cause gravitational bound objects to experience that expansion, so it was thought that the expansion of space only works in regions of space where there is no nearby source of gravity that could overcome the expansion of space.

No, that's not how it works. "The expansion of space" is not a "thing that is happening" in some places but not others. It's just another way of saying that comoving objects in our universe--objects that see the universe as homogeneous and isotropic--are moving apart.

 

[elcaro]

Please don't speculate. The model proposed in the paper under discussion is already speculative. Piling speculation on speculation is extremely unlikely to be fruitful. The best we can do at this point is to try to identify additional pieces of evidence or theoretical analysis that would help to evaluate the paper's proposal.

You are right of course - this reasearch is as of now aleady very speculative to say the least.

 

[elcaro]

Not to a black hole by the standard definition. The objects being called "black holes" in this context have no event horizons and no singularities. They look like black holes from the outside, but they only have apparent horizons, and the dark energy in their interiors prevents them from having singularities.

Ok, that is how I understood it.

A black hole horizon (meaning the event horizon of a standard black hole) is not the same as a cosmological horizon. The model proposed in the paper under discussion does not change anything about the cosmological horizon of our best current model of the universe.

Sorry for the misunderstading, I meant to say the evet horizon of the black hole, not the cosmological horizon.

That's correct. See above.

Ok. Then at least I understood that correctly.

 

[Ken G]

Yes. That's one of the reasons to be skeptical of the paper's claims, since there are multiple lines of evidence that indicate that it's highly unlikely that the ordinary matter content of our universe could have been as large in the past as it would have to be for the paper's proposed model to work.

I don't understand this point. The article is claiming that once a (small) amount of matter is turned into dark energy inside the black hole, they think it can "cosmologically couple" and increase the effective mass of the black hole with time. But I don't see how they could be thinking that the original matter content of the universe was any more than the standard model would say without cosmological coupling-- the baryon density in the early universe seems too well constrained for them to accept that picture. How are you computing what the ordinary matter content would have needed to be in order for their model to work?

 

[PeterDonis]

The article is claiming that once a (small) amount of matter is turned into dark energy inside the black hole, they think it can "cosmologically couple" and increase the effective mass of the black hole with time.

Yes, but the question is whether the coupling produces enough of an increase to account for the current fraction of dark energy.

How are you computing what the ordinary matter content would have needed to be in order for their model to work?

I haven't been able to find such a computation in the paper, but it's possible I've missed it. I am not entirely clear on how the coupling in their model is supposed to work.

 

[Ken G]

I don't think they know how it is supposed to work either, they just find that if the mass increases like a^3, then they can understand their observations (though other interpretations are possible), and the power of 3 dovetails with certain elements of GR solutions that are acting like dark energy inside the black holes. I think that's all they have to go on, so I believe their main purpose is to make a controversial suggestion to try to stimulate GR theory to answer the very question you are asking, in hopes that if a solution with coupling and dark energy built into it can be made consistent with an accelerating boundary and high spin, then it will all sort of come together somehow. It's a tall order, certainly, but the advantage is that it solves a host of other issues:
-- how black holes can be consistent with quantum mechanics (they don't need singularities)
-- how black holes can accrete faster than the Eddington rate (they don't need to)
-- what is the dynamical origin of dark energy (it emerges from the solution that doesn't exist yet)
-- why is the expansion accelerating (it is a self-consistent behavior stemming from some kind of preference that the universe is showing to this solution that doesn't exist yet)

Along the way, the quest for this new solution might solve another problem: there is currently no black hole solution that is appropriate to the universe in which we live, even if the eventual GR solution doesn't work out as they are hoping. And one must admit, there has been an enormous amount of debate about what happens inside event horizons, it's just a shame Hawking isn't still here to weigh in on what he thinks this all means.

 

[PeterDonis]

there is currently no black hole solution that is appropriate to the universe in which we live

There is the Schwarzschild-de Sitter solution. Granted, our universe is not exactly de Sitter, but it will approach it more and more closely as time goes on. It's true that even that solution still has a singularity, though. The only way to avoid a singularity once a trapped surface (i.e., an apparent horizon) is present is to have an equation of state that violates the energy conditions that are assumed in the singularity theorems, which dark energy does. So I do think that some kind of solution along those lines will end up becoming part of our best current model.

 

[Ken G]

Then all that's left is the issue of whether or not it induces cosmological coupling with b about 3. There's also the issue that most black holes spin quite fast, so high spin might have some different elements, that's what the authors seem to think could be true but I have no idea! It would sure be weird if the answer ever looks like "the expansion of our universe is accelerating because of the angular momentum carried by gas falling into black holes." Not a sentence I ever expected to hear myself say.

 

[fhenryco]

Something that may be went unnoticed in this discussion is that in the cited theoretical paper by Crocker &all even though the action is that of GR, the way the field equations are derived is not the usual way: for instance to get the new Friedmann like equations they are not extremizing the action under variations of the total metric field and then average , but they instead extremize under variation of the conformal scale factor already from the begining (as if it was treated as a standalone scalar field): that's why pressure inside compact objects can now source their New kind of Friedman equations which is not the case in GR. So it's not strictly speaking the GR we know.