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

[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.