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

[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.

 

[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.