Dark energy from supermassive black holes? Physicists spar over radical idea

Let me explain. When we talk about cosmology in general and the (accelerated) expansion of the universe in particular, we zoom out to very large scales and consider a homogenous model of the universe (a so-called FLRW spacetime[0]). Here, homogeneity means that mass density, hubble rate and so on are the same across the universe and only depend on time.

We then deduce that at this scale and under these assumptions we need to incorporate an additional parameter Λ, called cosmological constant aka dark energy, into our field equations / cosmological solution in order to match observations.[1]

Homogeneity was a simplifying assumption, though! Our universe is clearly not homogeneous! Next to your head, there is air, and inside your head evidently not :), and so the mass density is clearly not constant across space!

The same thing holds for black holes: Outside a black hole there's vacuum, inside a black hole there is… Well, we don't really know but the mass from which it formed has gotta be somewhere, right? So the mass density in black hole spacetimes is presumably not constant, either.

Interestingly, we know that spacetime near other celestial bodies (galaxies, stars, planets, moons, …) can be approximately described by one of the black hole spacetimes, too. (This is because outer region of black hole spacetimes describes not just black holes but any spherically or axially symmetric static/stationary spacetime.) So it's turtl—… uhh outer black hole spacetimes all the way down!

Anyway, in those cases of stars/planets/moons we have some massive object in the center of the spacetime region and vacuum outside – once more, the mass density is clearly non-zero!

So how do we square this with the homogeneity assumption of our cosmolical model (ΛCDM)? We can't but that's perfectly fine from a logical point of view. The reason is that we cannot simply take all those local spacetimes (of all stars, planets and black holes) and simply add them up to obtain the spacetime of the entire universe, because the field equations are not linear. Adding up two solutions does in general not yield a third solution! Conversely, we cannot simply zoom in on the FLRW spacetime and then compare a local, perfectly homogeneous "snippet" of FLRW with a black hole spacetime – this comparison does not make sense a priori.

Unfortunately, the reality is we simply don't know how to zoom in / zoom out between different spacetimes at different scales. So while we have a cosmological constant at large scales (when assuming homogeneity), there is no guarantee such a constant makes sense at smaller scales, i.e. that there is expansion at smaller scales.

This is because there are two possible ways to interpret the cosmological constant: One way is to interpret it as a fixed parameter in the field equations (i.e. it influences every solution), another way is to interpret it as a term in the specific large-scale spacetime solution of our universe (i.e. ΛCDM) and shove it into that solution's energy-momentum tensor.

Now, I think most physicists adhere to the first interpretation and assume that the constant is the same across all scales and possibly even homogeneous. Thus it should impact all spacetime solutions in the same way and at all scales, including black hole solutions.

For this reason people have introduced modified black hole solutions that, like our cosmological model, take into account a positive cosmological constant (= "de Sitter"), for instance

https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschil...

As you suspected, in these solutions you generally have both effects that counteract each other: The gravitational pull of the black hole (leading to an event horizon) and the expansion of the universe ("anti-gravitational pull") due to the cosmological constant, leading to a cosmological horizon in the region far away from the black hole.

Nevertheless, whether you believe in/consider a cosmological constant at small scales is a bit up to you. Most people I know seem assume that space at the level of atoms, planets, solar systems or even galaxies is not expanding and only very far away from gravitational systems you'll end up with expansion. This is supported by the fact that the cosmological constant is so tiny and, thus, in the aforementioned De Sitter black hole solutions, the cosmological horizon is far, far away from the center – so far indeed (111 (M/Msolar)1/3 parsecs[2]) that we know this outside region of the spacetime can no longer be valid/applicable.

To see the latter, remember that black hole solutions assume a perfect vacuum away from the central body (black hole/star/planet/…) but in reality no massive body is alone in the universe. This means that, before you reach a distance of 111 (M/Msolar)1/3 parsecs from a given body, you'll long have encountered another couple massive bodies which will modify your spacetime and cause additional gravitational pull. (Once again, how exactly they modify spacetime we don't know (short of maybe some numerical approximations), since we can't easily superpose spacetimes!)

Long story short: Only in very few situations it's worth considering a cosmological constant at small scales. Its effects are easily cancelled out / hidden by local gravity.

[0]: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

[1]: https://en.wikipedia.org/wiki/Lambda-CDM_model

[2]: https://ui.adsabs.harvard.edu/abs/2020AAS...23537904F/abstra...

No. That's not how the spacetime geometry around black holes works.

The example in the talk was that “spacetime expanding” and “matter shrinking” are mathematically equivalent, and the choice is merely a preference between interpretations.

Said differently, how the expansion of the universe looks like at the human scale? Most probably the quetsion does not make sense (?)

There is no limit to how high this pressure can go, as there are always higher energy states to occupy. (Except that for electrons at a high enough energy state, they will disappear by fusing with protons.)

For neutrons, there is no such disappearing effect, so the degeneracy pressure can keep on increasing. So how can this pressure ever be "overcome by gravity"?

Apparently at some point the degeneracy pressure itself starts to contribute significantly to spacetime curvature. This increases gravitational pressure, which compresses the neutrons, which increases the degeneracy pressure, which increases curvature, etc. No balance is possible anymore and collapse happens.

Presumably this process of ever increasing neutron degeneracy pressure continues within the black hole until unknown physics come into play.

[chatGPT]> There is currently no evidence to suggest that dark energy can be compressed into a small volume and exhibit a gravitational pull in the same way that ordinary matter does. Dark energy is thought to be a property of the vacuum of space itself, and its effect on the universe is driven by its negative pressure, which causes the universe's expansion to accelerate.

Black hole masses are measured by observing their gravitational effects on surrounding matter and other astronomical objects. The mass of a black hole can be estimated by measuring the velocity of nearby stars or gas clouds and using the laws of gravity to infer the mass of the object producing the gravitational field. These measurements are based on our current understanding of gravity and are not affected by the presence or absence of dark energy.

However, it is worth noting that the properties of dark energy are still not fully understood, and there may be some new discoveries or developments in our understanding of gravity that could change our current understanding of these phenomena. Nonetheless, as of now, there is no evidence to suggest that dark energy can contribute to our measurements of black hole masses through its gravitational effects.

[chatGPT]> While it is true that gravity is not perfectly homogeneous across the universe, this alone does not explain dark matter or dark energy.

Dark matter is believed to exist because of the observed gravitational effects on galaxies and galaxy clusters that cannot be accounted for by the visible matter alone. These observations suggest that there is additional matter that we cannot see, which we call dark matter. While gravity may vary in strength in different regions of the universe, this alone cannot explain the observed gravitational effects that we attribute to dark matter.

Similarly, dark energy is believed to exist because of the observed accelerating expansion of the universe. While variations in gravity across the universe could play a role in this phenomenon, they cannot explain the magnitude of the effect that we observe.

In summary, while variations in gravity across the universe are a real phenomenon, they cannot fully explain the observed effects attributed to dark matter and dark energy. These mysteries continue to be the subject of active research in the field of astrophysics and cosmology.

There are bounds on the size and quantity of such black holes, which get increasingly tight as more data on dark matter becomes available.

Most of that has been ruled out (see the graph on http://resonaances.blogspot.com/2016/06/black-hole-dark-matt... ) and while some black holes may fall into the dark matter category, the observed "if there were that many black holes, micro lensing would be this common..."

The result of those tests constrains black holes to less than 1% of the calculated dark matter... though there are some windows where there is very likely active research to try to detect black holes with those masses along with the cosmological models needed to have an early universe that produces black holes of that size in that quantity.

From https://arxiv.org/pdf/2007.10722v3.pdf

> Primordial Black Holes, in particular asteroid mass ones, remain a viable dark matter candidate. Further improve- ments in the theoretical calculations of the production and evolution of PBHs are required to reliably predict the abundance and properties of PBHs from a given model. Even so, it seems clear that a cosmologically interesting num- ber of PBHs can only be produced in specific models of the early Universe, and often fine-tuning is required. However, whether or not PBHs are a significant component of the DM is a question that has to be answered observationally. Novel ideas are needed here to either detect or rule out the remaining open parameter space.

Note that we're dealing with really small ones that haven't evaporated yet.

The chart on page 16 - with M PBH [g] and the X axis of 10^15 to 10^36 - that's grams.

Also fun - https://github.com/bradkav/PBHbounds which has them in solar masses

> Obviously, I don't have an explanation myself, and I understand that we can only work with the evidence we have, but I think it's a sign we need to radically rework our basic assumptions about reality, and not just look for our missing keys...

Looking for missing keys is fine. This is how models are validated or invalidated. For example, Neptune's location was predicted in the 19th century before it was observed due to discrepencies in Uranus' observed orbit and what was modeled.

There are alternative theories that could replace dark matter/dark energy (e.g. MOND for dark matter, inhomologous cosmologies for dark energy).

The universe is expanding. However, not only is it expanding, but the expansion is accelerating. It isn't clear what is driving this, and source of the acceleration was given the name dark energy.

The "dark" in these names are part we don't know what these things are yet and part we can't see them yet with our current observational methods.

> I find it kind of funny that humans are so confident that our models of reality are correct

I don't think this is the case. If you have another model that replaces general relativity, I think people would be very interested in it. People have tried several times to explain the observations that led to dark matter by modifying various forms of gravity. They all work less well than general relativity. So the search continues: keep adjust the models but also don't be afraid that there are new things in the universe that we didn't previously know about. There are several experimental approaches that are searching for ways to directly detect dark matter.

Sure. You seem to take issue with this notion. However, this very strategy lead to the discovery of elementary particles (neutrino) and planets (Neptune) in the past. It's how science works.

> Obviously, I don't have an explanation myself, and I understand that we can only work with the evidence we have, but I think it's a sign we need to radically rework our basic assumptions about reality, and not just look for our missing keys...

This is an extremely common opinion among laymen (relevant: https://xkcd.com/1758/). I find it a bit patronizing, because it implies that scientists haven't considered everything under the sun to explain the observations. Please take it from me, who got a PhD in cosmology, that every single person I encountered during my graduate studies was extremely bright, in particular the professors. They have thought of everything a layman can think of a billion times over. The knowledge gap in a field as unintuitive as cosmology between a professor and a layman is basically that of an adult and a toddler.

That's not saying that dark matter or dark energy is beyond any doubt, just that "we need something radically different" is not a very helpful take. You're basically saying "We just need another Einstein", except better data is harder and harder to come by. It's not sufficient anymore to just observe the perihelion shift of mercury. We now need to do things like measure the shapes of billions of galaxies to make any progress, and hope that the billions of galaxies we can observe (there is an upper bound) will yield sufficient precision to even tell two theories apart. We need to build gigantic particle accelerators and build humongous particle detectors in the antarctic to even hope to make some progress.

That's not how it works.

Many a physics PhD has spent their career trying to come up with better models, including different sorts models of gravity or indeed "to radically rework our basic assumptions about reality,".

Surprisingly, physics professors aren't idiots and have thought of this. It's just that, so far, invisible matter is still the thing that best fits the data compared to the (non-overfitted) modified gravity models people have been able to come up with so far.

Dark Matter is just a hypotheses to explain our current observations. Future discoveries may back up dark matter, or point towards something different. This is how Science works.

I think you’re oversimplifying, like seeing a forest and overlooking that it’s Prototaxites, not Malus domestica.

Here’s Sabine Hossenfelder’s curious-undergraduate-level history of Dark Matter theories:

https://youtu.be/4_qJptwikRc

Proper nouns include Renzo’s Rule and Baryonic Tully Fisher Relation.

We know how gravity works locally (for various definitions of local). We can calculate and predict with a lot of accuracy how objects in our immediate vicinity will behave.

All of the evidence is pointing to confirmation of our understanding of the situation.

Then this bullshit star three dozen light years away says "fuck that noise" and does something completely wild. Either we're wrong about all of our math or we missed something.

The "we missed something" crowd is the "dark energy"/"dark matter" people. And by "dark", they just mean "undetectable by current instruments". They believe our math is right. I believe the other crowd is the "Grand Unified Theory" people. That the math itself changes at scale.

And why is "85% of matter is undetectable at distance" not transformative to our assumptions? Do you realize the implications of that? That if 85% of what we should be able to perceive is imperceptible, then the "great silence" may be here sooner than we expect. Maybe that 85% is stuff that is just beyond the speed at which we'd be able to perceive it.

The models used aren't used because scientists think they are correct, but because they are the best models that fit existing experimental data. Best normally meaning 'simplest that explain all data', but it isn't quite always that simple. There are scientists who spend the latter parts of their careers trying to find even better models or even proposing worse models that are useful to keep in a folder somewhere in case they ever do become relevant or we come across data the current model can't explain. At the cutting edge of science you even find that the current models aren't matching all the data, but there is no consensus on a better model and scientists are working to either expand or replace the current model to fit the new data and to explore the non-matching data to either see if it is an error (which does happen) or if it gives hints on a better model.

Anyone who thinks that the model is correct is someone who is lacking a foundation in what science is saying. Often scientists don't talk about the distinction because it is too detailed for the public to care about, but that's not the same as not recognizing the distinction. (Much like how programmers talk about computers as if they are intelligent beings making decisions, often to the programmer's detriment, despite any good programmer knowing that isn't the case, newest models of AI tentatively excluded.)

It makes so much more sense that there's no Dark Matter.

I think the title of fine.

Some synonyms of spar are argue and quarrel. This isn't ridiculous editorializing.