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I've read the recent news about non-Kerr black holes coupling to the universe's expansion rate, and it looks like an excellent fit to the data. From the paper, I understand that these black holes grow with the universe's expansion rate to the third power in the absence of accretion, as observed, and that they predict a cosmological constant of about \Omega_V = 0.7, which is also spot on.

What I don't understand is the model. The black holes don't contain singularities, but are "filled with vacuum energy." Following the references back, I didn't understand the original theory papers, apart from the statement that these black holes can't spin, which I think is in contradiction with gravitational wave detections.

Does anyone here understand the model well enough to explain to general physicists, or better yet, undergraduate or high school level? "Filled with vacuum energy" isn't helpful, since all of space is filled with vacuum energy. What's special about black holes in this model?

Jim Pivarski
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    I also am waiting for enlightenment , with bated breath. – anna v Feb 18 '23 at 08:04
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    This and the answers might be relevant https://physics.stackexchange.com/questions/682414/is-there-a-gr-explanation-for-cosmological-coupling-causing-mass-increase-as-the . It is a different proposal but the same double counting might happen – anna v Feb 18 '23 at 08:14
  • A lot of these papers, including the ones referenced in the question you link to (thanks!) were written by the same (but growing) group of people. The paper I think is the foundational one is https://doi.org/10.3847/1538-4357/ab32da, which claims that the Kerr solution is incompatible with asymptotic space-time curvature (the Kerr solution's asymptote is a non-expanding space-time). So this new compact object, originally called "GEODE", was motivated by asymptotic behavior and "just happens" to solve the dark energy problem. It would be amazing if it did! – Jim Pivarski Feb 18 '23 at 15:45
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    But one has to go into their calculations relating the theory with the data. It is possible that they get a good fit with the small omega_lamda, via double counting something, because it has been an input to the calculations – anna v Feb 18 '23 at 17:22
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    Yes, I think this paper is wrong in the same way as the one in the question that anna v linked. They're starting with a background of critical-density matter, then adding another critical density's worth of black holes etc. on top of it. The claim that the Kerr geometry is inconsistent with an expanding universe makes no sense. The claim that something inside the black hole could mimic dark energy is inconsistent with Birkhoff's theorem. – benrg Feb 19 '23 at 09:33
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    @benrg That sounds like a pretty elementary error. Do you think something that simple would have made it past the peer reviewers? Moreover, this article quotes two astrophysicists who seem receptive to claim, and even Bob Wald seems to object based on the grounds of quantitative disagreement and somewhat technical issues of stability, not on the grounds of a fundamental conceptual error like double-counting. – tparker Feb 23 '23 at 05:30
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    @benrg I don't mean to come across as skeptical - my question above does not presume an answer, but is an honest request for your opinion. I know that the peer review process has serious problems and massive mistakes slip through all the time. But the likelihood of such a fundamental conceptual error varies significantly between journals, and I'm not familiar enough with this particular journal to gauge the likelihood that that occurred in this case. – tparker Feb 23 '23 at 05:34
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    @tparker For what it's worth, I wrote another answer about the paper by Croker and Weiner that OP linked in an earlier comment, and this about a paper by Cooperstock, Faraoni and Vollick. Croker and Faraoni are coauthors of this paper. I'm sure CFV is wrong because I can reproduce their conclusion from my assumption about what they did wrong. I think CW is wrong because their assumptions don't seem to make sense (even they say the assumptions are inconsistent with the existence of Kerr black holes), and because the swiss-cheese model seems to be a counterexample. – benrg Feb 24 '23 at 01:39
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    @tparker I don't know what to say about the papers being published. I think they're wrong, published or not. – benrg Feb 24 '23 at 01:40
  • I can't assess the correctness of the Farrah et al paper or @benrg's rebuttal, but I have to say, this whole situation is socially weird. The Farrah result is presented in the news media as a breakthrough. The news media is often wrong about science, but usually by inflating a 1.5-sigma excess as a discovery. That's not what's happening here: if the claim is true, it is a major turning point. If it's obviously wrong, you'd expect a backlash of mainstream physicists setting the record straight, because it is such a big claim. But all I see is the original claim copy-pasted with no response. – Jim Pivarski Feb 24 '23 at 14:48
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    Also, for what it's worth, my original question was just asking what the authors mean. As an experimental particle physicist, I can't understand the paraphrase "filled with vacuum energy," because what makes that different from empty space? I also haven't been able to understand the GEODE model, presented in its technical glory, from which the phrase "filled with vacuum energy" presumably derived. Even a wrong model is something we can talk about at different levels of technical sophistication. I was hoping to get an explanation between the levels of the news media and the original paper. – Jim Pivarski Feb 24 '23 at 14:54
  • When both @benrg and Ethan think a hot new take is wrong/100% unsound, I pay attention. – Mr Anderson Sep 10 '23 at 03:44
  • How can there be a event horizon without a singularity?? – Cerise Sep 16 '23 at 01:34

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They proposes that all small-scale inhomogeneity should contribute to the pressure term in the Friedmann equations, including the pressure within the cores of compact objects. Let us write the perfect fluid equation of state (EOS) as

$$ P = \omega \rho \,,$$

where $P, \rho$ stands for pressure and density while $\omega$ is a const. They hypothesize that black holes are not really black holes, but instead, some compact objects with their interior having an EOS with $\omega = -1$ (e.g., Gravastars - black hole mimickers with de-Sitter interior). As a result, these objects would contribute to the cosmological EOS.

With this assumption, they then further assume that if their mass $m$ follows the trend (where $a$ is the cosmic scale factor and $t_i$ the cosmic time when the black hole was born)

$$ m(t) = m(t_i) \left( \frac{a(t)}{a(t_i)} \right)^3 \,,$$

hence deserving the name "cosmological coupling", then to respect the principle of stress-energy conservation, it becomes necessary that they contribute to the cosmological pressure, which will be equal to the negative of their energy density. This pressure will have a similar effect on the universe's expansion, akin to the influence of dark energy.

They then show that with a standard population of stellar mass black holes alone, one can reproduce the accelerated expansion effect along with the value of $\Omega_\Lambda$.

Interestingly, in this paper, they then show observational evidence for their proposed mass growth trend by looking at supermassive black holes residing at the centers of elliptical galaxies. They, therefore, conclude that "black holes" are the source of accelerated expansion.

However, up till now, there has been severe criticism of their claim on many accounts.

S.G
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  • Thanks for the explanation! From Wikipedia, I saw that [https://doi.org/10.3390/universe9020088] is a recent overview paper and all of the recent observations of black hole properties from LIGO and EHT (https://physics.stackexchange.com/q/477319/7770) don't contradict this black hole alternative. Has any explanation been proposed about why collapsing bodies would have this structure, why a negative-pressure fluid would develop instead of a traditional black hole? Or is this just beyond all experimental bounds and therefore "there be dragons"? – Jim Pivarski Sep 15 '23 at 17:39
  • It is a hypothesis that maybe the quantum nature of black holes would lead to a phase transition (akin to the Bose-Einstein condensate phase transition) in their interiors and, therefore, result in a system that is singularity-free and also does not lead to information paradox, etc. As it turns out the Gravastar proposal has been successful in recreating the outside geometry of the Schwarzschild black hole and, at the same time, not having an internal singularity or information loss problems. E.g. see https://arxiv.org/pdf/gr-qc/0310107.pdf – S.G Sep 15 '23 at 23:19
  • Maybe I should direct this objection to the authors, but the equation of state of the interior of an object says nothing about the equation of state of a collection of such objects. If you filled a bunch of perfectly mirrored hollow balls with radiation, the collection of balls would still behave as matter. – Sten Sep 16 '23 at 05:13
  • @Sten that is a very valid objection. This is in a way their claim - that it does matter, e.g. see their 2017 paper. – S.G Sep 16 '23 at 05:18