> He also says the numbers don’t seem to add up: Dark energy is known to make up 70% of the mass-energy of the universe, whereas black holes are a mere fraction of the ordinary matter, which constitutes less than 5% of the universe
So it seems both the missing dark energy and the missing dark matter could both be explained for, if there were far more black holes in our universe than we're currently aware of?
Black holes are a known explanation for dark matter (until recently not for dark energy, as black holes were in the end still thought of as a bunch of dense matter).
There are bounds on the size and quantity of such black holes, which get increasingly tight as more data on dark matter becomes available.
Primordial black holes used to be a dark matter candidate but have been largely ruled out. This has been extensively studied already. They'd be anything but supermassive, though. The exact opposite, to be precise.
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.
> 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.
Nonsense. Inside the global warming field there are loads of different models and predictions and intense debate about different ideas.
There are some outlier models that are ignored by other scientists because of their bad faith assumptions and methodology but that's true of many fields of science like quantum physics and cosmology.
Wrong. Scientists trying to get funding for projects exploring things like the impact of sun radiations on earth climate, have a very hard time because of the political rules that are enforced in terms of what's allowed to be looked at and what's not.
Scientists are also tired of arguing about the reality of evolution, perpetual motion mechanisms, flat earth, a non-plate techtonic earth and maybe other settled matters. Try to get a research fellowship for flat earth or perpetual motion and see just how ruthlessly science cuts down dead ideas. Or maybe now in Florida you can get a flat earth fellowship, the Republicans certainly seem eager to remove the benefits of our scientific learnings as fast as they can.
Scientists choose to argue about things like did Eukarya evolving from Archaea?Imagine having interesting debates about that [0] and then having some numpty tell you that evolution doesn't exist at all.
>Dark energy is known to make up 70% of the mass-energy of the universe, whereas black holes are a mere fraction of the ordinary matter, which constitutes less than 5% of the universe.
Is there some cosmological constraint that says dark energy compressed into a small volume would exhibit gravitational pull and therefore contribute to our measurements of black hole masses? If not then it feels like this is a weak counterargument that makes a pretty big assumption that dark energy must have the same mass-energy equivalence behaviour as regular energy from a general relativity perspective. If black holes somehow are the origin of dark energy, then surely this is driven by physics at energies far beyond our understanding from either particle physics or cosmology. In that case aren't basically all bets off in terms of what you'd expect to observe in terms of apparent black hole masses?
Well the whole idea is to "make it work" under the constrains of our current understanding (General Relativity). After all , all that Dark Energy is by definition is something that is Contrasting the Gravity as described by general Relativity. If we remove that fact than it doesn't need to be reconciled with anything really. Saying that it is a type of energy that doesn't behave according to general Relativity, you need to solve a much bigger problem, find the Substitute of General Relativity that would work for all cases and in that scenario maybe even Gravity is different and you don't even need Dark Energy.
Not that I'm aware, but there are modified GR theories. In classical GR, the equations can be derived by applying the principle of least action with the Ricci scalar R being the Langrangian. People are studying what happens if you assume the Lagrangian is a function of R, like R^n or so. It doesn't have the same stigma as MoND, but it's also not that popular. It's also very hard to test for.
>Is there some cosmological constraint that says dark energy compressed into a small volume would exhibit gravitational pull and therefore contribute to our measurements of black hole masses?
[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.
Correct me if I'm wrong (please), but don't we still lack any kind of fundamental definition of what dark energy/matter is other than..."the cause of the difference between what is calculated, and what is observed"? To the point that we aren't even really sure that there is such a "thing" as dark matter (in that it exists in any conventional sense)?
From Wikipedia: "Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe...The primary evidence for dark matter comes from calculations showing that many galaxies would behave quite differently if they did not contain a large amount of unseen matter. Some galaxies would not have formed at all and others would not move as they currently do."
85% is kind of a lot of "stuff" to be missing...
I find it kind of funny that humans are so confident that our models of reality are correct that we truly think it's more likely there's just hidden "stuff" than there's just something hugely wrong with our idea of what the universe really is, and how it works. Our physics works great in a lot of circumstances, but to be missing 85% of the damn universe might imply we are wildly off base when it comes down to the true nature of things.
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...
Perhaps black holes are the right place to look, but not as a cubby hole for our missing stuff - rather, as a path to transforming our assumptions about reality.
> "the cause of the difference between what is calculated, and what is observed"
Dark energy / the cosmological constant Λ is a completely natural parameter to the field equations, not a corrective term (even though it might feel that way if you follow the history of cosmology). It's not that we calculated Λ to be zero but observations forced us to set it to something non-zero. We had no clue what it's value should be and simply deduced from observations that it happens to be non-zero. End of story.
Now, particle physicists / field theorists have been looking for a particle physics-based explanation for Λ and preliminarily called it "dark energy". But there's no guarantee there is one. Maybe Λ is indeed just a boring parameter.
> I find it kind of funny that humans are so confident that our models of reality are correct that we truly think it's more likely there's just hidden "stuff" than there's just something hugely wrong with our idea of what the universe really is.
> 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).
Dark matter is the name for unexplained mass that doesn't interact like typical matter. The existence of such mass is needed because there are galaxies that don't match what is predicted by general relativity. So either general relativity is wrong on the particular predications or there is extra matter.
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.
> People have tried several times to explain the observations that led to dark matter
The observations that led to Dark Matter have been sufficiently explained without the need for Dark Matter.[1] Apparently, subsequent observations that got lumped into Dark Matter have not yet been sufficiently explained, and Science is paradigmatic, so Dark Matter persists.
> Correct me if I'm wrong (please), but don't we still lack any kind of fundamental definition of what dark energy/matter is other than..."the cause of the difference between what is calculated, and what is observed"?
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.
> I find it kind of funny that humans are so confident that our models of reality are correct that we truly think it's more likely there's just hidden "stuff" than there's just something hugely wrong with our idea of what the universe really is, and how it works.
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.
I mean, we already know about existing "dark" matter particles. The Neutrino comes to mind, though it's not massive enough to explain the gravitational phenomena. LCDM really isn't that weird or unexpected, since it's a lot like what we already observe, and we already think more particles should exist.
They are, because they have mass and don't interact electromagnetically. They are just not cold dark matter, because their mass is so low they behave more like radiation than matter, i.e. the scale as a^4 instead of a^3, where a is the scale factor. A sterile neutrino, if it existed, could still be a dark matter candidate.
Hypothetical "dark matter" doesn't interact with ordinary matter, except gravitationally. Neutrinos do interact with ordinary matter; otherwise we wouldn't be able to build neutrino detectors. Therefore neutrinos are not an example of dark matter.
> "dark matter" doesn't interact with ordinary matter, except gravitationally.
It's possible that this is the case, but particles that also interact with the weak force (hence WIMPs: weakly interacting massive particles) are generally considered better candidates.
You'd be hard pressed to derive a model for the coarse structure of the universe from the Standard Model, considering the Standard Model can't describe gravity. Maybe this is part of the problem..
Every one of those parameters is associated with a field that does symmetry breaking. Every one of those fields has a particle associated. Every one of those particles has been observed, studied, and found to have properties in line with what would be required for the fields to have the values that we measure.
So yes, that's a lot of free parameters. But they are intrinsic to the theory. And we have considerable experimental evidence that they represent something real.
For those who don't know what symmetry breaking is, the Standard Model has a lot more symmetries than the observed universe. For example the theory does not specify that electromagnetism is long range while the strong nuclear force is short range. Or that the muon weighs more than the electron. But for each symmetry in the theory that we don't see in practice, there is a field that specifies the value of the observed asymmetry. Each field is carried by a particle. Each particle has properties that reflect the value of all of the fields. Every particle has been found and almost all have the predicted properties (to within measurement error).
The last particle found was the Higgs boson. The Higgs field determines the relative masses of different particles.
The "almost all" is the fact that the neutrino has 3 versions and oscillates between them in flight. Also the neutrino is not massless. While the Standard Theory can adapt to match this, this isn't what was originally predicted.
Right, and some physicists have a nagging feeling that the addition of another symmetry would result in the reduction in free parameters. "We've done it before, so why shouldn't it work again?" is their thought process. So they devise a model which replicates the standard model in observable ranges and to make it testable, doesn't replicate the standard model outside of the observable range. This is an attempt to make the model falsifiable and thus scientific. Then they advocate for expensive accelerators to falsify the model.
"...humans are so confident that our models of reality are correct..."
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.
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.
>I find it kind of funny that humans are so confident that our models of reality are correct
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.)
I'm a layman, but I like this idea intuitively. It's not mentioned in the article, but this theory also necessitates that black holes aren't singularities, which gets rid of what always seemed to me like the biggest hack in physics.
I've always wondered if the "horizon" metaphor in event horizon was more apt than we expected - just like when you approach the earth's horizon, you don't get flattened or fall off, you just reveal more geography - I've always wondered if it were possible that as you approach an event horizon you don't get "squashed into spaghetti" but just reveal more space which is just as "normal" as the space before you approached the horizon. But caveat - i have no real reason to actually believe this is true - I'll assume for now it's just poetic.
The "squashed into spaghetti" occurs in "normal space" before you get to the black hole, for most black holes. It is not an effect of anything special about black holes, it's just plain ol' normal tidal effects, turned up to eleven, then turned up until the knob breaks, then turned up some more. Neutron stars will give you a bad day with tidal effects too long before you reach their surface.
Very large black holes turn out not to have this, though it's going to be a long time cosmologically before there are any large black holes also quiet enough for you to get anywhere near.
To an outside observer it would look like you were torn apart by tidal forces, but would it feel that way to you? Or would you feel normal? If it's just space being curved, would you feel nothing just like you feel nothing in freefall? I'm sure this question is wrong...
The "tidal effect" here is due the difference in gravity experienced by parts of you at different distances from the gravity source.
Imagine your feet pulled downward hard enough that your bones stretch and/or snap, while you are squished in from the sides. And then more. You'd become a long thin strand of matter, no longer in the shape of a human and no longer feeling anything. It's not "just a ride down" where things feel locally normal, and it's not a phenomenon about black holes, as some stars can do that to you too.
Position is relative, velocity is relative, acceleration is actually absolute. Tidal forces are not relative, they are agreed upon by all observers, who would all agree that you got torn apart by those forces. You can remember this by considering the effect acceleration has on objects; there is no trajectory an object can take in which it will observe the surface of the earth being at 25G and consequently everything being crushed on it. They'll still see 1G, they just won't agree about the velocities being modified and in sufficiently extreme cases, won't agree about how long the forces were applied for, but they'll still see 1G.
Being able to witness varying accelerations would actually be a very strange theory, having instead a twin paradox in which one astronaut takes off and comes back home to a twin (and civilization) crushed to death, whereas the stay-at-home twin sees his twin take off, get crushed to death, and never return home at all. The YouTube videos trying to explain this universe would certainly be epic.
Again, this all happens in normal space too; the black-hole-ness of the black hole is not in play yet. Non-black hole objects can "spaghettify" too.
I don't have a specific link. But the larger the black hole, the lesser the tidal forces at the event horizon. Tidal forces are created by gravity gradients, the differences, and the differences become less extreme as the black hole sizes up. You can see it just by thinking about how the gravity field changes around an object as it gets larger; think about where the 1G line as you make the Earth denser and denser, and note how quickly the field is changing at that point. Hypothetically, a large black hole would permit you to actually survive entry into the event horizon. It's still hypothetical because the environment around any such black hole in the current era is still far too violent for you to get that close, and it will be for cosmologically-meaningful periods of time.
The tricky part with black hole spaghettification is that the slope of the gravity gradient (tidal force) can be pictured as exceeding 90 degrees within the event horizon, because there is no speed limit for the flow of space. This doesn't violate physics because Einstein's speed of light limit only applies to matter moving within space. This idea has been embraced by astrophysicists to explain inflation at the start of the Big Bang.
Why this matters is that when something spaghettifies, the particles at the end can never catch up to the ones at the beginning. The space between the ends of the spaghetti grows. Which also means that the spaghetti can never reach the pit at the center of the black hole, because the pit is farther ahead in its journey.
So our intuition that falling into a black holes means that we'll collide with the center is incorrect. If we could survive the journey, we'd see ourselves falling forever towards something growing infinitely farther away. Like trying to catch up with a falling elevator that's moving faster than we are.
From the outside, we see anything falling in as becoming 2D on the surface, red shifting as it accelerates away from us, becoming time dilated until it appears to freeze, never quite reaching the speed of light from our frame of reference. So even though it's being stretched along the radial axis and perspective should make it look smaller over time as our separation grows, it appears to stay the same size to us as it was when it entered the event horizon.
So a black hole can be thought of as an infinitely long tunnel to.. somewhere.
I prefer to think of it as a bubble which only grows internally. So in a very real sense, a whole universe is being birthed inside.
Unfortunately the math breaks down near the singularity, so maybe the particles do see themselves colliding with a pit. For example, the sun is 8 light minutes from Earth, so even if it was heavy enough to collapse into a black hole, it should still take 8 minutes to reach the center for a particle falling towards it, from its frame of reference.
But I don't think that's how it works. I think that the space flowing in faster than the speed of light overcomes spaghettification, creating a maximum strain inversely proportional to the mass of the black hole. Hawking hinted at this when he thought about what would happen to a human falling into a billion solar mass black hole whose tidal forces are weak enough that they're survivable.
-- edit: this paragraph is wrong, the universe behind also red shifts, which I realized after considering that the object's watch and ours are synchronized during free-fall --
Probably what happens is that the object sees the universe behind it speed up faster and faster as it blue shifts, until it ends in a white-hot flash the number of light-seconds away that the object began falling. Meanwhile the space ahead appears to expand in the same way as inflation, creating a pocket universe containing the mass which has already fallen in. Except that the universe behind appears to also red shift, due to the increasing distance between the object and anything behind. The expansion and contraction probably balance to create a microwave background at a temperature inversely proportional to the age of the universe inside. So the background inside might be hotter than ours since the black hole is smaller than the parent universe.
----
Also if nothing more falls into the black hole and it starts evaporating, matter inside will see previously fallen matter growing away from it. Just like how we see stars and galaxies moving away from us faster than the speed of light when their distance times the Hubble constant exceeds the speed of light, causing our universe to grow lighter and expand faster, which we perceive as dark energy. So matter inside would eventually see the perimeter rushing towards it faster and faster as the black hole loses its mass, with its internal Hubble constant growing larger and larger until the expansion of...
If the ends of the spaghetti can never reach each other after space's rate of stretching passes the speed of light, then the spaghetti can never reach the pit. If the spaghetti never reaches the pit, then everything in the black hole falls forever. If everything falls forever, then the clock outside the block hole is synced to the clock of particles falling inside the black hole.
Which suggests that a black hole forms an infinitely deep funnel, and if we entertain the idea that the rules of our universe keep working inside it, an hourglass.
What does that look like? On Earth, space pours down our gravity well, reaching a stagnation point sometime before the center, which forms an indentation in spacetime which we ride in as we orbit the sun.
In a black hole, there's still a stagnation point, if we consider the entire life of the black hole, including final evaporation. The bottom of the indentation falls at the speed of light, but eventually slows and rebounds as the black hole begins to shrink due to Hawking radiation, then springs back into our reality. In other words, the space inside a black hole is more dynamic than where we are.
We're normally shown a picture of that falling floor tearing through our spacetime into an unknown place. But since the space is falling faster than the speed of light, I think that it crosses over itself and diverges, forming a white hole on the other side. The math of that white hole matches the math of the Big Bang. So we can picture the child universe as starting just like ours, and forming a sphere in the bottom of the hourglass expanding faster than the speed of light until its density gets low enough that the expansion proceeds at merely the speed of light. The same way that inflation worked in our universe.
Particles at the edge of the sphere are able to leak back into the parent universe via Hawking radiation just like our galaxies at great distance slip out of our universe red-shifted faster than the speed of light. So the mass of the sphere begins to shrink, which slows its rate of expansion. Eventually its space starts to contract, [turning the child Hubble constant negative] <- edit: increasing its Hubble constant even higher. Everything begins to contract back towards one another. The edge of the sphere eventually rushes back inwards at the speed of light, creating a Big Crunch.
It's not that matter is crushed together, but that space is contracting so fast out from under it that it has nowhere else to go but back up out of the throat. The final pop is reverse spaghettification, as each particle is torn apart back to quarks, electrons and energy back into the parent universe. The hard part to visualize is that the crunch happens inward towards each particle simultaneously, there is no center.
The quantum mechanical aspect and notions like the Planck length are probably a distraction. An electron is always a point charge roughly the size of its uncertainty, in any spacial coordinate system. Maybe it has more mass and is a muon or tau (or something heavier), but it never stops being an electron fundamentally. When it spaghettifies in the throat, its wave function only has 2 degrees of freedom, along the radial axis and rotation, with the third degree along the time axis. Until space diverges again in the white hole on the other side and it's able to exist in 3D again.
So our universe is the white hole on the other side of the black hole in the parent universe, and the universe is infinite, looking like swiss cheese with child universes and more black holes inside the bubbles. The centers of atoms may act like miniature black holes, but with slightly different rules involving the electroweak force and probability, creating an emergent force which we think of as the strong for...
I'm afraid so. I'll just pick on two important ways found in one of your key sentences, and I'll stick to widely accepted results from Hawking, Unruh, Gibbons and Giddings.
> Particles at the edge of the sphere are able to leak back into the parent universe via Hawking radiation just like our galaxies at great distance slip out of our universe red-shifted faster than the speed of light.
Firstly, Hawking radiation doesn't leak anything out of the black hole itself; it's produced by interactions between the outside matter fields and the dynamical spacetime outside an evolving black hole. Secondly, you have the relevant part of cosmic horizons backwards. They also produce a form of Hawking radiation in the far future.
So, since nothing ever comes from inside the black hole's horizon even at final evaporation, or from outside the cosmic horizon, I don't see how you can recover your more cosmological ideas.
"One way of achieving a better understanding of [why black holes seem to behave by thermal objects and evaporate by emitting Hawking radiation] is to study the origin of particles in black hole evaporation, .i.e., the question of where they are created." [authors' emphasis]
The paper goes on to show that because Hawking radiation is a low-energy process, the origin of particles must be from a distance outside the horizon proportional to the radiation wavelength, and cannot originate very close to the horizon (much less from inside it). This follows from his earlier conference presentation <https://inspirehep.net/literature/775859> (pdf available at <https://pos.sissa.it/043/039/>), "Where are the particles created in Black Hole evaporation?"
"Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon ... However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale".
The last clause there is expanded in the text:
"... the source of Hawking radiation is a quantum region of size \Delta r ~ R outside the black hole horizon"
R there means the Schwarzschild radius, so particles originate in a fairly voluminous region with the lower edge at about a Schwarzschild radius above the black hole's horizon, i.e., at about 2R.
Also a layman. Doesn't singlarity mean a place/time where our math/models break down? It's not a hack, but a place/time our understanding fails. It's not meant to mean something physical.
Could gravity not being homogenous across universe explain dark matter/energy?
What if law of gravity has other terms that only reduce to the versions we think of as true in the scenarios we've tested...but the other terms are affecting things of supermassive scale?
What if there is some other "force" between things cosmically that we have never seen on the scales we've done stuff...but that we can observe (but misinterpret as dark stuff) on galactic/cosmic scales?
What if quantum correlation produces a "force" among particles that's only apparent on super massive scales? If all particles used to be close together in the big bang, couldn't they have some lingering correlations? Or became correlated with movement of electricity through cosmic web?
>Could gravity not being homogenous across universe explain dark matter/energy?
[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.
I'm still convinced that there's a huge gap in general relativity since it seems that "dark matter/energy" with no material evidence whatsoever is exactly that final correction term.
Here's a question I'm not even remotely qualified to ask: could it be that supermassive black holes cause a contraction of local spacetime in a way that gives the impression that local space is static while distant space expands?
I think this mechanism would be largely indistinguishable from classic hubble expansion, at least on local scales.
That's a good question and is not exactly easy to answer. The Einstein field equations of General Relativity are highly non-linear which makes it difficult to talk about superpositions of solutions to the equations and to compare local physics (at the level of black holes) to cosmological effects (e.g. the expansion of the universe) and transfer results and insights between them.
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
> 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?
Not in the standard black hole model with a singularity at the center, no. In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed. The interior of the hole is vacuum, just like the exterior.
In the alternative "black hole" model being used in the proposed hypothesis for dark energy, no singularity is ever formed; instead, the collapsing matter undergoes a kind of phase transition (probably induced by quantum field effects of some sort) that changes its equation of state from that of normal matter to that of dark energy. This stops the collapse and creates an object that, at least on time scales much shorter than the Hawking evaporation time scale (since these objects will eventually evaporate by emitting Hawking radiation), looks from the outside like a standard black hole, though it isn't. The dark energy inside such objects, it is proposed, could drive accelerated expansion of the universe.
> Not in the standard black hole model with a singularity at the center, no. In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed. The interior of the hole is vacuum, just like the exterior.
If the interior of a black hole becomes a vaccume, what continues to assert the intense gravitational pull that the now destroyed matter once created?
I'm not the OP but I mentioned this briefly in my other comment[0]: Even vacuum black holes carry mass. As a starting point, search for "ADM mass" or have a look at Wikipedia. [1]
Yeah. I see you are asking some of the same questions. After reading, the best answer I could find is that "quantum vacuum" is totally different than "classic vacuum".
But what this really means I haven't figured out yet.
The other person[0] responded to this thread by saying something like the curvature of space-time is curved, and there is no gravity in GR. So OK, but what causes the curvature if not mass / matter..?
On a different note: We don't need to bring in quantum mechanics ("quantum vacuum") here. General Relativity is a purely classical (i.e. non-quantum) theory and doesn't care about quantum mechanics. So the vacuum we're talking about here is the "classic vacuum".
> If the interior of a black hole becomes a vaccume, what continues to assert the intense gravitational pull that the now destroyed matter once created?
The spacetime geometry of the hole. The "pull" you describe is a property of the spacetime geometry. Gravity is not a force in GR, so the "pull" is not being caused by an interaction with matter. Objects moving solely under gravity simply move on geodesics of the spacetime geometry.
I understand that. But what CAUSES the geometric curvature in the first place. Not mass? If the blackhole is then a vacuum, surely it has no mass and thus there is nothing to curve space time around it.
Replace my question with space-time curvature:
"If the interior of a black hole becomes a vacuum, what continues to assert the intense space-time curvature that the new destroyed matter once created?"
1. The simplest black hole solutions in General Relativity are eternal black holes in vacuum. Yes, you read that right: There is no mass and yet they live forever (and have lived forever). There is no way to say why that is other than: The field equations permit these solutions, so they are possible (at least in principle).
The thing is: Nothing in the field equations says there has got to be matter for your spacetime to have curvature. The spacetime just has to fulfill the equations. If you set the energy-momentum tensor in the equations to zero (i.e. there is no matter), you end up with the equation Ric = 0, where Ric is the Ricci tensor, and it turns out that this equation has non-trivial solutions. "Non-trivial" here means: Non-trivial curvature (i.e. not flat) and/or non-trivial topology (e.g. not infinite volume like 4D Minkowski space).
For instance, apart from the curved black hole solutions, you could also have non-trivial flat solutions with the topology of a 4D torus/donut, i.e. with a finite volume.
Why do these solutions exist? Well, because each of them fulfills Ric = 0. Put differently, your question basically amounts to asking "Why do spheres exist if there are planes?" (Both are the solution to the 2D equation k = 0, where k is 2-dimensional (sectional) curvature.)
-- Intermezzo --
Let me approach your question from a slightly different angle: You are understandably surprised that vacuum black hole (i.e. curved) solutions exist because you associate curvature with gravity and have learned that curvature comes from matter ("matter curves spacetime and curvature is gravity"). But this only have the story:
No one ever said that curvature has to come from matter. What's more, gravity is a very narrow, human-invented term that comes from pre-relativistic times when apples were falling from trees. See, the fundamental thing about General Relativity is not that matter curves spacetime or gravity is curvature but that
1) the universe is a 4-dimensional object ("Lorentzian manifold" in math speech) which fulfills the Einstein field equations and which we call spacetime, and that
2) in the absence of other forces (i.e. in free fall), objects follow the equivalent of straight lines ("geodesics") in that spacetime.
In this sense, even the flat vacuum (Minkowski space) has "gravity": It's just very boring gravity because the geodesics are actual (Euclidean) straight lines: An object will stand still in 3D space and only move in time.
In short: Gravity doesn't care about the spacetime being curved or non-curved. It's always there. It's just that in human, practical terms, we call one situation (falling down from a tree) "gravity" and another one (standing still in empty 3D space) "absence of gravity" but from the perspective of General Relativity there is no real difference: Both are spacetimes with geodesics.
So is it surprising that there are curved spacetimes without any matter in them? I don't think so.
-- Intermezzo end --
Back to our eternal black hole solutions in vacuum: As I mentioned, not only do they live forever but they also have lived forever, so there are not exactly great models for reality as we have yet to encounter a black hole that's ∞ years old.
This brings us to the second case:
2. In realistic models of black holes (i.e. black hole formation) we don't really know what happens to the matter once it passes the event horizon. General Relativity predicts the matter will hit the singularity in finite time ("finite proper time") but in reality we have no clue what happens there.[0] Maybe it vanishes, maybe it does another thing entirely (because of quantum-gravitational effects or who-knows-what).
So I'm not sure I would go as far as saying once a black hole has formed, the situation is similar to one of those vacuum black holes wher...
> what CAUSES the geometric curvature in the first place.
The object that collapsed to form the black hole.
> If the interior of a black hole becomes a vacuum, what continues to assert the intense space-time curvature that the new destroyed matter once created?
Nothing has to. The curvature maintains itself once it is formed by the collapsing matter. This is an example of an effect of the nonlinearity of the Einstein Field Equation.
> In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed
Sure, but that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior. That's why I phrased it that way.
It doesn't matter, though, even if you say the matter inside the black hole no longer exists (and I'm very happy to entertain that thought): Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density.
> that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior
While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. That's why the phase transition I mentioned, to an equation of state corresponding to dark energy, is necessary to avoid forming the singularity and leaving only vacuum in the interior--because the dark energy equation of state violates the energy conditions that are premises of the singularity theorems.
> Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density.
Sure, but this "mass" is not due to the continuing presence of matter somewhere inside the hole. It's a property of the spacetime geometry.
> While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them.
Sure but it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow. So I think you'll see why I'm a bit sceptical about your claim that
> the collapsing matter that formed the hole hits the singularity and is destroyed
I don't even know what "destroyed" is supposed to mean. Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities?
As for:
> The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter.
Do they? The Singularity Theorems assume the existence of a trapped surface. Last I checked[0] (I didn't check deeply, though) the mathematical results on when trapped surfaces arise are very few and far between. Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually?
[0]: This was in 2020 when the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
> it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow
Yes, but that doesn't change what the model says. It just affects how likely we think it is that the model is actually realized in our universe. I agree that it's quite likely that the standard black hole model I described isn't realized in our actual universe. But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness.
What's of great interest about alternate models for collapsed objects that have dark energy inside, like the Bardeen "black hole", is that they do hold out the promise of being a better model to replace the standard black hole model, that doesn't have a singularity anywhere and so would not be expected to break down the way we think the standard black hole model breaks down near the singularity.
> Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities?
The matter disappears, but conserved quantities do not. They remain embedded in the spacetime geometry that is left behind.
> The Singularity Theorems assume the existence of a trapped surface.
Yes, but the alternate "black hole" models with dark energy inside, such as the Bardeen "black hole", also have trapped surfaces, so this doesn't help to distinguish the models.
The singularity theorems also assume energy conditions. Those are the conditions that the models with dark energy inside violate, and which allow those models to not have singularities even though they do have trapped surfaces.
> Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually?
I don't know about "proof", but there are plenty of numerical simulations of realistic collapses of massive objects like stars that show trapped surfaces forming. So I would say it's a robust expectation of any such collapse process, even if we don't have an ironclad proof that it must occur in every single case.
> the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
That statement was justified. But saying that it's a robust prediction if particular conditions are satisfied is not the same as saying that all of those conditions must be satisfied in our actual universe.
> But saying that it's a robust prediction if particular conditions are satisfied
But that's not what they said. They said (or implied) it's a robust prediction of GR for our actual universe.
> But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness.
But I never questioned the usefulness of the whole rest of GR? GR is a beautiful and much more satisfying, consistent and mathematically rigorous theory than e.g. QFT, so only because we know its predictions might not hold near singularities I wouldn't dare throwing out the baby with the bathwater. I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity. And it looks like we agree here.
> They said (or implied) it's a robust prediction of GR for our actual universe.
Who is "they"? The people who published the singularity theorems didn't say that. They only said the theorems are mathematically valid given the assumptions, and they proved that by proving the theorems. They didn't say the assumptions had to be satisfied in our actual universe. In fact, most physicists say the opposite: that the mathematical validity of the singularity theorems shows that at least one of the assumptions they are based on must be violated in our actual universe, since it would be physically unreasonable for there to be singularities in our actual universe.
> I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity.
In the sense that most physicists believe a singularity is physically unreasonable, yes, I agree. But in the absence of a better model, that doesn't help very much. The nice thing about the hypothesis under discussion here is that it holds out the prospect of a better model, if it can be made to work.
Preamble: we are largely on the same page. I thought I'd draw your (or our mutual readers') attention to a couple details where we may differ a little.
> [link to wikipedia's de Sitter-Schwarzschild page]
Let's call it Schwarzschild-de Sitter (SdS, for short, and for ease of literature-searching).
More generally there is the McVittie family of metrics of a massive object in a dynamical spacetime. SdS is the limiting case of McVittie where the spacetime is stationary and the central mass is compact, spherically symmetric, 0-angular-momentum, and uncharged. (One could alternatively say that McVittie is a generalized time-dependent SdS.)
> black hole solutions assume a perfect vacuum
Not quite, but this is mainly a specialist quibble, since the most widely known theoretical black holes are vacuum or electrovac spacetimes. See for example the Kerr-Vaidya black hole solutions, which have either a incoming radiation ("null dust") field or an outgoing one (or both) falling onto resp. shining out of ("roughly Hawking") a spinning black hole. There are many other nonvacuum solutions with a compact central mass (which can look more or less black-hole-like), both exact and non-exact.
The important feature of these is asymptotic behaviour, as you touch on in your second-last paragraph, since if the influence of the central mass fades with distance, and the sources are kept distant from each other, that lets us ignore (but see below) the difficulties in combining two or more exact solutions of the Einstein Field Equations into a new exact solution.
Linearized gravity is usually applicable and sufficient, and if not one can obtain corrections using post-Newtonian theory. We don't really need numrel unless mass-ratios are small and compactness is extreme. See the handy diagram at <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...>.
See also Ellis 2010 (Chapter 2, section 3 on inexact solutions, notably his complaint at the bottom of p. 34 to the top of p. 35) <https://doi.org/10.1017/CBO9780511622724.002>, which is handily also at s c y h o b. Re his complaint see also Visser 2014 on horizons: <https://arxiv.org/abs/1407.7295>.
You're right, I should have been more precise here. I was merely trying to say: The spacetimes in the vicinity of celestial bodies can be modeled sufficiently well by vacuum black hole solutions (obviously as long as we don't get too close and don't need to consider accretion disks, radiation and what not).
... or actual surfaces, which we are allowed in Kerr (or more properly perturbations thereof) or Hartle-Thorne spacetimes where the central body is non-compact, for example.
Where modelling an astrophysical body this way tends to fall down is that as far as we can tell the central mass evolves and is in general not uniform in the sense that it has long-lasting multipole moments (that would quickly bald away for a black hole), frustrating the hopes of matching the object's interior with the exterior solution. In comparison, outer space is practically always empty enough of stress-energy that the non-physicality of the vacuum or lambdavac region is rarely the issue (and can be dealt with perturbatively, for example).
The other major problem is that binary (and triple) systems are surprisingly commonplace, and the N-body problem will drive one towards approximations of GR for tractability. This is the essence of this thread's cautions on the difficulties in superposing solutions to the EFEs. Worse, the two problems above can feed into one another, like when binary stars raise long-lived bumps on each other.
> could it be that supermassive black holes cause a contraction of local spacetime in a way that gives the impression that local space is static while distant space expands?
No. That's not how the spacetime geometry around black holes works.
There is nothing in the mathematical description of a black hole (whether a normal black hole or the "black hole" like objects with dark energy inside them that are proposed in the alternative model being discussed here) or the physics that that math describes that corresponds to the ordinary language description "a contraction of local spacetime in a way that gives the impression that local space is static while distant space expands".
I once watched a nice talk about how scientists can inadvertently get “stuck” in a particular point of view because interpretations are often an A/B choice where both are valid. After taking a long path through many such interpretation choices it’s easy to loose track of the alternative points of view.
The example in the talk was that “spacetime expanding” and “matter shrinking” are mathematically equivalent, and the choice is merely a preference between interpretations.
I believe that is backwards...time changes due to gravity and not vice versa. It's a misunderstanding propagated in the last few years through misconceptions.
around the turn of the century many ideas were floating around in order to explain unexplainable phenomena. It took Einstein and Quantum physics to radically change the worldview and make sense, while make-shift ideas were discarded.
What is going on with titles? Do physicists really put on boxing gloves hoping that physical violence will resolve a scientific argument? Is this a new widely accepted approach?
I find this level of editorializing ridiculous to the point of insulting.
I don’t need the imagery of violence to boost my curiosity about a new discovery.
If sparring incites images of violence for you, I suspect you don't really understand what sparring is. It's specifically practice without the violence -- extra rules are put into place to ideally eliminate injury, though of course accidents do happen.
This reminds me of a question I’ve had for a while, and have not been able to formulate it well enough to do any searching for an answer on my own (total layman here).
Do we have any hypotheses of what the matter inside a black hole might be like? I mean “hypotheses” in a strict sense; I do not mean “a good/definitive answer”
To oversimplify a bit: white dwarves are supported by electron degeneracy pressure, and if such pressure is exceeded by gravity then e.g. a neutron star can form. Neutron stars are supported by neutron degeneracy pressure, and if such pressure is exceeded by gravity then a black hole can form.
For each of those “steps” we have an idea of what the matter within must be like to support/exceed such pressures. Are there any hypotheses for what the matter might be like after such known pressures are exceeded and a black hole is formed?
Degeneracy pressure comes from the Pauli exclusion principle.
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.
115 comments
[ 1.4 ms ] story [ 212 ms ] threadSo it seems both the missing dark energy and the missing dark matter could both be explained for, if there were far more black holes in our universe than we're currently aware of?
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
In the end it may turn out that black holes are the source of both dark energy and dark matter.
https://youtu.be/-8CIUzPkigQ
There are some outlier models that are ignored by other scientists because of their bad faith assumptions and methodology but that's true of many fields of science like quantum physics and cosmology.
0 - https://www.sciencedirect.com/science/article/pii/S096098222...
Is there some cosmological constraint that says dark energy compressed into a small volume would exhibit gravitational pull and therefore contribute to our measurements of black hole masses? If not then it feels like this is a weak counterargument that makes a pretty big assumption that dark energy must have the same mass-energy equivalence behaviour as regular energy from a general relativity perspective. If black holes somehow are the origin of dark energy, then surely this is driven by physics at energies far beyond our understanding from either particle physics or cosmology. In that case aren't basically all bets off in terms of what you'd expect to observe in terms of apparent black hole masses?
https://en.wikipedia.org/wiki/F(R)_gravity
[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.
From Wikipedia: "Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe...The primary evidence for dark matter comes from calculations showing that many galaxies would behave quite differently if they did not contain a large amount of unseen matter. Some galaxies would not have formed at all and others would not move as they currently do."
85% is kind of a lot of "stuff" to be missing...
I find it kind of funny that humans are so confident that our models of reality are correct that we truly think it's more likely there's just hidden "stuff" than there's just something hugely wrong with our idea of what the universe really is, and how it works. Our physics works great in a lot of circumstances, but to be missing 85% of the damn universe might imply we are wildly off base when it comes down to the true nature of things.
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...
Perhaps black holes are the right place to look, but not as a cubby hole for our missing stuff - rather, as a path to transforming our assumptions about reality.
In particular, dark energy is not
> "the cause of the difference between what is calculated, and what is observed"
Dark energy / the cosmological constant Λ is a completely natural parameter to the field equations, not a corrective term (even though it might feel that way if you follow the history of cosmology). It's not that we calculated Λ to be zero but observations forced us to set it to something non-zero. We had no clue what it's value should be and simply deduced from observations that it happens to be non-zero. End of story.
Now, particle physicists / field theorists have been looking for a particle physics-based explanation for Λ and preliminarily called it "dark energy". But there's no guarantee there is one. Maybe Λ is indeed just a boring parameter.
> 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.
The observations that led to Dark Matter have been sufficiently explained without the need for Dark Matter.[1] Apparently, subsequent observations that got lumped into Dark Matter have not yet been sufficiently explained, and Science is paradigmatic, so Dark Matter persists.
[1] https://www.youtube.com/watch?v=PL0ewiwqoTw
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.
We are fundamentally missing something. Thankfully it’s just not all that important for us right now.
It's possible that this is the case, but particles that also interact with the weak force (hence WIMPs: weakly interacting massive particles) are generally considered better candidates.
So yes, that's a lot of free parameters. But they are intrinsic to the theory. And we have considerable experimental evidence that they represent something real.
For those who don't know what symmetry breaking is, the Standard Model has a lot more symmetries than the observed universe. For example the theory does not specify that electromagnetism is long range while the strong nuclear force is short range. Or that the muon weighs more than the electron. But for each symmetry in the theory that we don't see in practice, there is a field that specifies the value of the observed asymmetry. Each field is carried by a particle. Each particle has properties that reflect the value of all of the fields. Every particle has been found and almost all have the predicted properties (to within measurement error).
The last particle found was the Higgs boson. The Higgs field determines the relative masses of different particles.
The "almost all" is the fact that the neutrino has 3 versions and oscillates between them in flight. Also the neutrino is not massless. While the Standard Theory can adapt to match this, this isn't what was originally predicted.
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.)
Very large black holes turn out not to have this, though it's going to be a long time cosmologically before there are any large black holes also quiet enough for you to get anywhere near.
Imagine your feet pulled downward hard enough that your bones stretch and/or snap, while you are squished in from the sides. And then more. You'd become a long thin strand of matter, no longer in the shape of a human and no longer feeling anything. It's not "just a ride down" where things feel locally normal, and it's not a phenomenon about black holes, as some stars can do that to you too.
https://en.wikipedia.org/wiki/Spaghettification
Being able to witness varying accelerations would actually be a very strange theory, having instead a twin paradox in which one astronaut takes off and comes back home to a twin (and civilization) crushed to death, whereas the stay-at-home twin sees his twin take off, get crushed to death, and never return home at all. The YouTube videos trying to explain this universe would certainly be epic.
Again, this all happens in normal space too; the black-hole-ness of the black hole is not in play yet. Non-black hole objects can "spaghettify" too.
Technically true, according to current theories. The slope of spacetime gets steeper and steeper and you traverse through that spacetime as you go.
(Due to the gravity, you won't be whole to experience it.)
https://youtu.be/8-xODPI1OFg?t=253
Why this matters is that when something spaghettifies, the particles at the end can never catch up to the ones at the beginning. The space between the ends of the spaghetti grows. Which also means that the spaghetti can never reach the pit at the center of the black hole, because the pit is farther ahead in its journey.
So our intuition that falling into a black holes means that we'll collide with the center is incorrect. If we could survive the journey, we'd see ourselves falling forever towards something growing infinitely farther away. Like trying to catch up with a falling elevator that's moving faster than we are.
From the outside, we see anything falling in as becoming 2D on the surface, red shifting as it accelerates away from us, becoming time dilated until it appears to freeze, never quite reaching the speed of light from our frame of reference. So even though it's being stretched along the radial axis and perspective should make it look smaller over time as our separation grows, it appears to stay the same size to us as it was when it entered the event horizon.
So a black hole can be thought of as an infinitely long tunnel to.. somewhere.
I prefer to think of it as a bubble which only grows internally. So in a very real sense, a whole universe is being birthed inside.
Unfortunately the math breaks down near the singularity, so maybe the particles do see themselves colliding with a pit. For example, the sun is 8 light minutes from Earth, so even if it was heavy enough to collapse into a black hole, it should still take 8 minutes to reach the center for a particle falling towards it, from its frame of reference.
But I don't think that's how it works. I think that the space flowing in faster than the speed of light overcomes spaghettification, creating a maximum strain inversely proportional to the mass of the black hole. Hawking hinted at this when he thought about what would happen to a human falling into a billion solar mass black hole whose tidal forces are weak enough that they're survivable.
-- edit: this paragraph is wrong, the universe behind also red shifts, which I realized after considering that the object's watch and ours are synchronized during free-fall --
Probably what happens is that the object sees the universe behind it speed up faster and faster as it blue shifts, until it ends in a white-hot flash the number of light-seconds away that the object began falling. Meanwhile the space ahead appears to expand in the same way as inflation, creating a pocket universe containing the mass which has already fallen in. Except that the universe behind appears to also red shift, due to the increasing distance between the object and anything behind. The expansion and contraction probably balance to create a microwave background at a temperature inversely proportional to the age of the universe inside. So the background inside might be hotter than ours since the black hole is smaller than the parent universe.
----
Also if nothing more falls into the black hole and it starts evaporating, matter inside will see previously fallen matter growing away from it. Just like how we see stars and galaxies moving away from us faster than the speed of light when their distance times the Hubble constant exceeds the speed of light, causing our universe to grow lighter and expand faster, which we perceive as dark energy. So matter inside would eventually see the perimeter rushing towards it faster and faster as the black hole loses its mass, with its internal Hubble constant growing larger and larger until the expansion of...
https://www.livescience.com/dark-energy-could-lead-to-a-seco...
If the ends of the spaghetti can never reach each other after space's rate of stretching passes the speed of light, then the spaghetti can never reach the pit. If the spaghetti never reaches the pit, then everything in the black hole falls forever. If everything falls forever, then the clock outside the block hole is synced to the clock of particles falling inside the black hole.
Which suggests that a black hole forms an infinitely deep funnel, and if we entertain the idea that the rules of our universe keep working inside it, an hourglass.
What does that look like? On Earth, space pours down our gravity well, reaching a stagnation point sometime before the center, which forms an indentation in spacetime which we ride in as we orbit the sun.
In a black hole, there's still a stagnation point, if we consider the entire life of the black hole, including final evaporation. The bottom of the indentation falls at the speed of light, but eventually slows and rebounds as the black hole begins to shrink due to Hawking radiation, then springs back into our reality. In other words, the space inside a black hole is more dynamic than where we are.
We're normally shown a picture of that falling floor tearing through our spacetime into an unknown place. But since the space is falling faster than the speed of light, I think that it crosses over itself and diverges, forming a white hole on the other side. The math of that white hole matches the math of the Big Bang. So we can picture the child universe as starting just like ours, and forming a sphere in the bottom of the hourglass expanding faster than the speed of light until its density gets low enough that the expansion proceeds at merely the speed of light. The same way that inflation worked in our universe.
Particles at the edge of the sphere are able to leak back into the parent universe via Hawking radiation just like our galaxies at great distance slip out of our universe red-shifted faster than the speed of light. So the mass of the sphere begins to shrink, which slows its rate of expansion. Eventually its space starts to contract, [turning the child Hubble constant negative] <- edit: increasing its Hubble constant even higher. Everything begins to contract back towards one another. The edge of the sphere eventually rushes back inwards at the speed of light, creating a Big Crunch.
It's not that matter is crushed together, but that space is contracting so fast out from under it that it has nowhere else to go but back up out of the throat. The final pop is reverse spaghettification, as each particle is torn apart back to quarks, electrons and energy back into the parent universe. The hard part to visualize is that the crunch happens inward towards each particle simultaneously, there is no center.
The quantum mechanical aspect and notions like the Planck length are probably a distraction. An electron is always a point charge roughly the size of its uncertainty, in any spacial coordinate system. Maybe it has more mass and is a muon or tau (or something heavier), but it never stops being an electron fundamentally. When it spaghettifies in the throat, its wave function only has 2 degrees of freedom, along the radial axis and rotation, with the third degree along the time axis. Until space diverges again in the white hole on the other side and it's able to exist in 3D again.
So our universe is the white hole on the other side of the black hole in the parent universe, and the universe is infinite, looking like swiss cheese with child universes and more black holes inside the bubbles. The centers of atoms may act like miniature black holes, but with slightly different rules involving the electroweak force and probability, creating an emergent force which we think of as the strong for...
I'm afraid so. I'll just pick on two important ways found in one of your key sentences, and I'll stick to widely accepted results from Hawking, Unruh, Gibbons and Giddings.
> Particles at the edge of the sphere are able to leak back into the parent universe via Hawking radiation just like our galaxies at great distance slip out of our universe red-shifted faster than the speed of light.
Firstly, Hawking radiation doesn't leak anything out of the black hole itself; it's produced by interactions between the outside matter fields and the dynamical spacetime outside an evolving black hole. Secondly, you have the relevant part of cosmic horizons backwards. They also produce a form of Hawking radiation in the far future.
So, since nothing ever comes from inside the black hole's horizon even at final evaporation, or from outside the cosmic horizon, I don't see how you can recover your more cosmological ideas.
Now some technical detail:
The origin of Hawking radiation is well outside the horizon of the black hole. Quoting Unruh in <https://doi.org/10.1103/PhysRevD.78.041504> (corresponding to the preprint at <https://arxiv.org/abs/0804.1686>):
"One way of achieving a better understanding of [why black holes seem to behave by thermal objects and evaporate by emitting Hawking radiation] is to study the origin of particles in black hole evaporation, .i.e., the question of where they are created." [authors' emphasis]
The paper goes on to show that because Hawking radiation is a low-energy process, the origin of particles must be from a distance outside the horizon proportional to the radiation wavelength, and cannot originate very close to the horizon (much less from inside it). This follows from his earlier conference presentation <https://inspirehep.net/literature/775859> (pdf available at <https://pos.sissa.it/043/039/>), "Where are the particles created in Black Hole evaporation?"
Giddings makes the same point in <https://www.sciencedirect.com/science/article/pii/S037026931...> (open access, but easier to read as a preprint at <https://arxiv.org/abs/1511.08221>). From the abstract:
"Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon ... However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale".
The last clause there is expanded in the text:
"... the source of Hawking radiation is a quantum region of size \Delta r ~ R outside the black hole horizon"
R there means the Schwarzschild radius, so particles originate in a fairly voluminous region with the lower edge at about a Schwarzschild radius above the black hole's horizon, i.e., at about 2R.
On Hawking radiation from cosmic horizons, Gibbons and Hawking's 1977 paper 1<https://journals.aps.org/prd/abstract/10.1103/PhysRevD.15.27...> detai...
Could gravity not being homogenous across universe explain dark matter/energy?
What if law of gravity has other terms that only reduce to the versions we think of as true in the scenarios we've tested...but the other terms are affecting things of supermassive scale?
What if there is some other "force" between things cosmically that we have never seen on the scales we've done stuff...but that we can observe (but misinterpret as dark stuff) on galactic/cosmic scales?
What if quantum correlation produces a "force" among particles that's only apparent on super massive scales? If all particles used to be close together in the big bang, couldn't they have some lingering correlations? Or became correlated with movement of electricity through cosmic web?
[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.
https://news.ycombinator.com/item?id=34813141
I think this mechanism would be largely indistinguishable from classic hubble expansion, at least on local scales.
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
Not in the standard black hole model with a singularity at the center, no. In the standard black hole model, the collapsing matter that formed the hole hits the singularity and is destroyed. The interior of the hole is vacuum, just like the exterior.
In the alternative "black hole" model being used in the proposed hypothesis for dark energy, no singularity is ever formed; instead, the collapsing matter undergoes a kind of phase transition (probably induced by quantum field effects of some sort) that changes its equation of state from that of normal matter to that of dark energy. This stops the collapse and creates an object that, at least on time scales much shorter than the Hawking evaporation time scale (since these objects will eventually evaporate by emitting Hawking radiation), looks from the outside like a standard black hole, though it isn't. The dark energy inside such objects, it is proposed, could drive accelerated expansion of the universe.
If the interior of a black hole becomes a vaccume, what continues to assert the intense gravitational pull that the now destroyed matter once created?
[0]: https://news.ycombinator.com/item?id=34898647
[1]: https://en.wikipedia.org/wiki/Mass_in_general_relativity#ADM...
But what this really means I haven't figured out yet.
The other person[0] responded to this thread by saying something like the curvature of space-time is curved, and there is no gravity in GR. So OK, but what causes the curvature if not mass / matter..?
[0] : https://news.ycombinator.com/item?id=34899615
The spacetime geometry of the hole. The "pull" you describe is a property of the spacetime geometry. Gravity is not a force in GR, so the "pull" is not being caused by an interaction with matter. Objects moving solely under gravity simply move on geodesics of the spacetime geometry.
Replace my question with space-time curvature:
"If the interior of a black hole becomes a vacuum, what continues to assert the intense space-time curvature that the new destroyed matter once created?"
1. The simplest black hole solutions in General Relativity are eternal black holes in vacuum. Yes, you read that right: There is no mass and yet they live forever (and have lived forever). There is no way to say why that is other than: The field equations permit these solutions, so they are possible (at least in principle).
The thing is: Nothing in the field equations says there has got to be matter for your spacetime to have curvature. The spacetime just has to fulfill the equations. If you set the energy-momentum tensor in the equations to zero (i.e. there is no matter), you end up with the equation Ric = 0, where Ric is the Ricci tensor, and it turns out that this equation has non-trivial solutions. "Non-trivial" here means: Non-trivial curvature (i.e. not flat) and/or non-trivial topology (e.g. not infinite volume like 4D Minkowski space).
For instance, apart from the curved black hole solutions, you could also have non-trivial flat solutions with the topology of a 4D torus/donut, i.e. with a finite volume.
Why do these solutions exist? Well, because each of them fulfills Ric = 0. Put differently, your question basically amounts to asking "Why do spheres exist if there are planes?" (Both are the solution to the 2D equation k = 0, where k is 2-dimensional (sectional) curvature.)
-- Intermezzo --
Let me approach your question from a slightly different angle: You are understandably surprised that vacuum black hole (i.e. curved) solutions exist because you associate curvature with gravity and have learned that curvature comes from matter ("matter curves spacetime and curvature is gravity"). But this only have the story:
No one ever said that curvature has to come from matter. What's more, gravity is a very narrow, human-invented term that comes from pre-relativistic times when apples were falling from trees. See, the fundamental thing about General Relativity is not that matter curves spacetime or gravity is curvature but that
1) the universe is a 4-dimensional object ("Lorentzian manifold" in math speech) which fulfills the Einstein field equations and which we call spacetime, and that
2) in the absence of other forces (i.e. in free fall), objects follow the equivalent of straight lines ("geodesics") in that spacetime.
In this sense, even the flat vacuum (Minkowski space) has "gravity": It's just very boring gravity because the geodesics are actual (Euclidean) straight lines: An object will stand still in 3D space and only move in time.
In short: Gravity doesn't care about the spacetime being curved or non-curved. It's always there. It's just that in human, practical terms, we call one situation (falling down from a tree) "gravity" and another one (standing still in empty 3D space) "absence of gravity" but from the perspective of General Relativity there is no real difference: Both are spacetimes with geodesics.
So is it surprising that there are curved spacetimes without any matter in them? I don't think so.
-- Intermezzo end --
Back to our eternal black hole solutions in vacuum: As I mentioned, not only do they live forever but they also have lived forever, so there are not exactly great models for reality as we have yet to encounter a black hole that's ∞ years old.
This brings us to the second case:
2. In realistic models of black holes (i.e. black hole formation) we don't really know what happens to the matter once it passes the event horizon. General Relativity predicts the matter will hit the singularity in finite time ("finite proper time") but in reality we have no clue what happens there.[0] Maybe it vanishes, maybe it does another thing entirely (because of quantum-gravitational effects or who-knows-what).
So I'm not sure I would go as far as saying once a black hole has formed, the situation is similar to one of those vacuum black holes wher...
The object that collapsed to form the black hole.
> If the interior of a black hole becomes a vacuum, what continues to assert the intense space-time curvature that the new destroyed matter once created?
Nothing has to. The curvature maintains itself once it is formed by the collapsing matter. This is an example of an effect of the nonlinearity of the Einstein Field Equation.
Sure, but that's a model for which we don't have any observational evidence whatsoever since it's the black hole's interior. That's why I phrased it that way.
It doesn't matter, though, even if you say the matter inside the black hole no longer exists (and I'm very happy to entertain that thought): Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density.
While this is true, it's not a very strong statement. Physicists extend models all the time into domains where we can't directly test them. The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter. That's why the phase transition I mentioned, to an equation of state corresponding to dark energy, is necessary to avoid forming the singularity and leaving only vacuum in the interior--because the dark energy equation of state violates the energy conditions that are premises of the singularity theorems.
> Any sensible definition of mass of the vacuum black hole (i.e. not necessarily the ADM mass since it's defined at infinity but e.g. some definition of quasi-local mass) will still give a non-zero contribution to the mass density.
Sure, but this "mass" is not due to the continuing presence of matter somewhere inside the hole. It's a property of the spacetime geometry.
Sure but it's not every day that we extend models into a domain (near the singularity) where we know our model must eventually break down somehow. So I think you'll see why I'm a bit sceptical about your claim that
> the collapsing matter that formed the hole hits the singularity and is destroyed
I don't even know what "destroyed" is supposed to mean. Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities?
As for:
> The singularity theorems of GR guarantee that the key features of that model, the singularity and the collapsing matter getting destroyed in it, must be true as long as the collapsing matter has the equation of state of ordinary matter.
Do they? The Singularity Theorems assume the existence of a trapped surface. Last I checked[0] (I didn't check deeply, though) the mathematical results on when trapped surfaces arise are very few and far between. Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually?
[0]: This was in 2020 when the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
Yes, but that doesn't change what the model says. It just affects how likely we think it is that the model is actually realized in our universe. I agree that it's quite likely that the standard black hole model I described isn't realized in our actual universe. But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness.
What's of great interest about alternate models for collapsed objects that have dark energy inside, like the Bardeen "black hole", is that they do hold out the promise of being a better model to replace the standard black hole model, that doesn't have a singularity anywhere and so would not be expected to break down the way we think the standard black hole model breaks down near the singularity.
> Is the claim that the matter simply disappears from the spacetime, with all its conserved quantum numbers and other conserved quantities?
The matter disappears, but conserved quantities do not. They remain embedded in the spacetime geometry that is left behind.
> The Singularity Theorems assume the existence of a trapped surface.
Yes, but the alternate "black hole" models with dark energy inside, such as the Bardeen "black hole", also have trapped surfaces, so this doesn't help to distinguish the models.
The singularity theorems also assume energy conditions. Those are the conditions that the models with dark energy inside violate, and which allow those models to not have singularities even though they do have trapped surfaces.
> Is there a clear proof that in realistic models of black hole formation we must have a trapped surface eventually?
I don't know about "proof", but there are plenty of numerical simulations of realistic collapses of massive objects like stars that show trapped surfaces forming. So I would say it's a robust expectation of any such collapse process, even if we don't have an ironclad proof that it must occur in every single case.
> the Nobel committee dubiously claimed that Penrose's Singularity Theorems prove that black hole formation and singularities "are a robust prediction of the general theory of relativity".
That statement was justified. But saying that it's a robust prediction if particular conditions are satisfied is not the same as saying that all of those conditions must be satisfied in our actual universe.
But that's not what they said. They said (or implied) it's a robust prediction of GR for our actual universe.
> But we can still use it if we don't have any better model to replace it with, since even if it breaks down near the singularity, that still leaves the whole rest of the model with plenty of usefulness.
But I never questioned the usefulness of the whole rest of GR? GR is a beautiful and much more satisfying, consistent and mathematically rigorous theory than e.g. QFT, so only because we know its predictions might not hold near singularities I wouldn't dare throwing out the baby with the bathwater. I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity. And it looks like we agree here.
Who is "they"? The people who published the singularity theorems didn't say that. They only said the theorems are mathematically valid given the assumptions, and they proved that by proving the theorems. They didn't say the assumptions had to be satisfied in our actual universe. In fact, most physicists say the opposite: that the mathematical validity of the singularity theorems shows that at least one of the assumptions they are based on must be violated in our actual universe, since it would be physically unreasonable for there to be singularities in our actual universe.
> I merely said we don't really know what's happening with the matter once it's inside the black hole / close to the singularity.
In the sense that most physicists believe a singularity is physically unreasonable, yes, I agree. But in the absence of a better model, that doesn't help very much. The nice thing about the hypothesis under discussion here is that it holds out the prospect of a better model, if it can be made to work.
> [link to wikipedia's de Sitter-Schwarzschild page]
Let's call it Schwarzschild-de Sitter (SdS, for short, and for ease of literature-searching).
More generally there is the McVittie family of metrics of a massive object in a dynamical spacetime. SdS is the limiting case of McVittie where the spacetime is stationary and the central mass is compact, spherically symmetric, 0-angular-momentum, and uncharged. (One could alternatively say that McVittie is a generalized time-dependent SdS.)
> black hole solutions assume a perfect vacuum
Not quite, but this is mainly a specialist quibble, since the most widely known theoretical black holes are vacuum or electrovac spacetimes. See for example the Kerr-Vaidya black hole solutions, which have either a incoming radiation ("null dust") field or an outgoing one (or both) falling onto resp. shining out of ("roughly Hawking") a spinning black hole. There are many other nonvacuum solutions with a compact central mass (which can look more or less black-hole-like), both exact and non-exact.
The important feature of these is asymptotic behaviour, as you touch on in your second-last paragraph, since if the influence of the central mass fades with distance, and the sources are kept distant from each other, that lets us ignore (but see below) the difficulties in combining two or more exact solutions of the Einstein Field Equations into a new exact solution.
Linearized gravity is usually applicable and sufficient, and if not one can obtain corrections using post-Newtonian theory. We don't really need numrel unless mass-ratios are small and compactness is extreme. See the handy diagram at <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...>.
See also Ellis 2010 (Chapter 2, section 3 on inexact solutions, notably his complaint at the bottom of p. 34 to the top of p. 35) <https://doi.org/10.1017/CBO9780511622724.002>, which is handily also at s c y h o b. Re his complaint see also Visser 2014 on horizons: <https://arxiv.org/abs/1407.7295>.
> > black hole solutions assume a perfect vacuum
> Not quite
You're right, I should have been more precise here. I was merely trying to say: The spacetimes in the vicinity of celestial bodies can be modeled sufficiently well by vacuum black hole solutions (obviously as long as we don't get too close and don't need to consider accretion disks, radiation and what not).
Where modelling an astrophysical body this way tends to fall down is that as far as we can tell the central mass evolves and is in general not uniform in the sense that it has long-lasting multipole moments (that would quickly bald away for a black hole), frustrating the hopes of matching the object's interior with the exterior solution. In comparison, outer space is practically always empty enough of stress-energy that the non-physicality of the vacuum or lambdavac region is rarely the issue (and can be dealt with perturbatively, for example).
The other major problem is that binary (and triple) systems are surprisingly commonplace, and the N-body problem will drive one towards approximations of GR for tractability. This is the essence of this thread's cautions on the difficulties in superposing solutions to the EFEs. Worse, the two problems above can feed into one another, like when binary stars raise long-lived bumps on each other.
This reminds me to re-read the invigorating <https://link.springer.com/article/10.1007/s00190-016-0927-4> which compares the gravitation of Earth and its messy multibody neighbourhood with several exact vacuum solutions and a couple of formalisms. The first author is the redoubtable Michael Soffel <https://www.iau.org/administration/membership/individual/733...> A PDF of the paper can also be found at s c y h o b. The kicker is the two paragraphs before section 3.
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 (?)
It makes so much more sense that there's no Dark Matter.
I suspect the same will happen with Dark Matter
I find this level of editorializing ridiculous to the point of insulting.
I don’t need the imagery of violence to boost my curiosity about a new discovery.
I think the title of fine.
Some synonyms of spar are argue and quarrel. This isn't ridiculous editorializing.
Do we have any hypotheses of what the matter inside a black hole might be like? I mean “hypotheses” in a strict sense; I do not mean “a good/definitive answer”
To oversimplify a bit: white dwarves are supported by electron degeneracy pressure, and if such pressure is exceeded by gravity then e.g. a neutron star can form. Neutron stars are supported by neutron degeneracy pressure, and if such pressure is exceeded by gravity then a black hole can form.
For each of those “steps” we have an idea of what the matter within must be like to support/exceed such pressures. Are there any hypotheses for what the matter might be like after such known pressures are exceeded and a black hole is formed?
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.