Mathematicians prove Hawking wrong about the most extreme black holes | Hacker News Reader

Mathematicians prove Hawking wrong about the most extreme black holes

quantamagazine.org

148 pointsworldvoyageur68 comments

" In principle, a black hole can reach a point where it has as much charge or spin as it possibly can, given its mass. Such a black hole is called “extremal” — the extreme of the extremes.

These black holes have some bizarre properties. In particular, the so-called surface gravity at the boundary, or event horizon, of such a black hole is zero. "

It had been thought impossible for such black holes to exist. However, new work now demonstrates that such black holes are indeed possible.

None have been found, however. Though this seems unsurprising. How would you detect one?

>How would you detect one?

I wonder if the gravitational wave signature of a merger between an extremal black hole with something else would give us any clues.

You might see something that appears to fall into nothing, with observable massive fluctuations in gravity - anything close by would get disintegrated, observing such an event would result in a treasure trove of data, as long as it's very, very far away. The secondary damage would be something like a particle accelerator bubble on the scale of multiple solar systems.

But it would not be falling into "nothing". There is an accretion disc.

There can be an accretion disc, but it's not a necessary property for a black hole to have.

AIUI the tidal forces and spacetime distortion are such that any matter falling in inevitably breaks apart into an accretion disk. It should be impossible for a whole body to enter a black hole intact.

All this is for a spinning black hole, of course, which most (all?) are.

Tidal forces at the event horizon of supermassive black holes are negligible.

https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf

This type of black hole is similar to dark matter, in that it warps local spacetime, but at the surface, the gravity is null, there's a weird spacetime topology to it, from what I can understand (I am not a physicist). It would be invisible, and any mass that went in would see an equivalent ejection of energy out, and the form of that energy would be fascinating. If you shot a planet into one of those at relativistic speeds it'd be a totally different, more catastrophically massive explosion than anything we've ever seen, and the volume of space around it would present opportunities to study extreme energy physics. One of the weird features is that because it cannot contain any more energy or mass, it has to immediately expel any additions, so the form of the energy coming out would be interesting to observe.

No surface gravity doesn't mean no gravity at all, right? It sounds like objects can orbit them at a distance, but would lose attraction as they got closer.

It's a bit of a contradiction with the idea of a black hole, and brings the feature that you can observe its surface.

From what I gather, you are correct. Furthermore, as there is no actual surface to stand on the theoretical forces such a surface would exert on a body (centrifugal due to lateral acceleration, and also normal) cannot exist anyway, so there is no physical predictive element to the idea anyway.

Black holes (all spinning masses) cause frame dragging, which effectively acts as a force on objects near it. The effect is normally tiny (but has been measured in Earth orbit). Close to a rotating black hole the force is so strong it can even prevent light from orbiting in the opposite direction to the spin of the black hole itself.

"But black holes with a discernible charge have never been observed. It’s far more likely to see a black hole that’s quickly rotating."

Three properties completely describe a black hole: mass, spin, and charge.

It does not appear that charge will be useful in the question of an extremal black hole.

In considering spin, as velocity of matter approaches c (the speed of light), more energy is required to achieve less gain as c is approached.

Can a black hole spin at the speed of light? Can it spin faster?

> Three properties completely describe a black hole: mass, spin, and charge.

So it's like an elementary particle?

I think the precursor neutron star might be closer.

Neutron star is still composed of... neutrons. There is a hypothesised Quark star though.

Inside a black hole? Consider a neutron star with mass 1 gram less than needed for it to become a black hole. Since the neutron star is not (yet) a black hole, we can 'see' it. Send in the 1 gram and watch while the neutron star converts to a black hole where, as usually proposed, the mass that was the neutron star suddenly shrinks to the "singularity" at the center of the black hole.

Now, it appears that there is a huge change -- neutron star to a black hole -- from a small input, the 1 gram, that is, in math terms, there is a jump discontinuity.

There was something about the physics of the neutrons that kept the neutron star from shrinking to a singularity. Well, maybe that something also keeps that mass plus the 1 gram from shrinking to a singularity. That is, if there is no jump discontinuity, the inside of that black hole is essentially just like that neutron star.

We don’t know that an object with 1 gram less than needed to become a black hole will be a neutron star. There may be other denser states or matter in between, like quark stars or strange stars that are still not dense enough to become black holes.

Under GR it doesn’t matter since as the mass increases beyond a critical point an event horizon will form and all that matter will be compressed into a singularity regardless.

> watch while the neutron star converts to a black hole where, as usually proposed, the mass that was the neutron star suddenly shrinks to the "singularity" at the center of the black hole.

This "conversion" doesn't imply matter transitioning from one state to another. The main thing happening during transition to a black hole is that the light can't escape anymore - you see the star in one moment, and can't see it in another moment. Not necessarily because of some matter transition, but because it stops radiating light.

Singularity is a mathematical artifact, we don't know what's happening in the blackhole with matter and don't really care since it has no effect on the outside world.

I've seen many physicists draw that analogy.

I am trying to imagine what happens to a single contiguous mass that has both a part that is travelling at relativistic speeds, and a part that is not?

Maybe nothing much? From each parts point of view it is still simply in contact with it's neighbor and neither is moving relative to the other?

> In particular, the so-called surface gravity at the boundary, or event horizon, of such a black hole is zero.

In space-like coordinates the event horizon is always an infinite distance away, so you can never reach the event horizon anyway. Like an infinitely deep hole in space.

Checking this physics on this kind of thing is really hard. The math saying an object can operate does not tell you how the object comes into existence, for example.

>To understand the universe, scientists look to its outliers. “You always want to know about the extreme cases — the special cases that lie at the edge,”

Some of the books I've read recently touch upon things like quantum mechanics and black-holes and that kind of stuff.

As a decently technical person but with no formal training in physics, can I generally interpret the study of things like black-holes and quantum physics as the idea of understanding how the physical world behaves as we take limit towards zero or infinity? Is that a correct way to think about it?

For example, I've studied probability and statistics somewhat formally in undergrad. The idea that electrons taken on a distribution and are technically "nowhere" until they are observed (schrodingers cat) sounds just like the description of a continuous variable, or alternatively where you take limit on a discrete variable such that it approaches a continuous distribution. The probability of the variable being any value is technically 0 but its state can be observed. It's hard to "truly" comprehend in a realistic since but its what allows us to build statistical models of things

If you have the time maybe look towards a community college and take a modern mechanics class! I took one in undergrad and it gives you insight into special relativity and basic quantum. Though I don’t remember a lot of it, it was really exciting to be able to practice the math and be able to ask the professor my questions.

I feel like with these topics you need to dive into the details to gain a strong understanding but then you only realize how much there is to learn.

Black holes form before any infinities. They form when enough mass-energy occupies a small region of space. And neither quantity is infinity. Due to how energy is related to wavelength, and that we need smaller wavelengths to probe smaller, and because everything has wavelength, we get that smaller scales require more energy (this is a simplification but correct). At a certain small enough size, again not infinity, we get a black hole due to energy density of that region of space. And any more energy just makes a bigger black hole. So we can’t actually get endlesssly smaller scales. The singularity is also a mathematical one and not something most physicists claim exists physically. I mean as a related example, there’s no way to physically infinitely divide space so infinities of calculus don’t imply infinities of spatial division.

QM I’m less sure where you think infinities pop up physically? One interesting thing is you’d need an infinitely size measuring apparatus to have absolutely certain measurement results due to random fluctuations, but as per above we can’t have infinitely size devices except for infinitely sized black holes, which won’t really help us. A lot of this is said more rigorously by Nima Arkani Hamed in his recorded public lectures.

Thanks for that, that's super interesting.

With quantum mechanics it's just infinity in the opposite direction, going infinitely small. My very pedestrian understanding is that the field of quantum mechanics came about because people were having trouble explaining the behavior of atomic particles, particularly electrons, using newtonian mechanics, and quantum mechanics were able to explain everything in a more comprehensive framework. At first I always found the idea that electrons are 'nowhere' until they are observed very mysterious, but it made a lot more sense when I understood that probability densities are involved in qm equations. There's usually a similar source of confusion when we move from "probabilities" of discrete distrubutions, which is quite easy to understand, to probability densities, which can be done by taking limit of number of possible states to infinity, and where you can get "probabilities" larger than one.

Just to add to this -- In QM/QFT there is an inverse relationship between energy & distance, meaning small distances (or sizes) correspond to high energy interactions (see e.g. [1]). One consequence is that at small enough scale (the Planck scale), the energy scale gets so large that quantum gravity effects are expected to be non-negligible. Formulating a theory of quantum gravity that fits into the Standard Model of particle physics & agrees with general relativity is an open problem in physics, therefore the Planck scale is at least the smallest distance that can conceivably be modeled given our current knowledge.

[1] https://physics.stackexchange.com/questions/731971/equivalen...

"going infinitely small"

My personal guess at a first-cut resolution:

An electron moves as a wave that satisfies Schrödinger's equation. Maybe that wave goes through a Young's double slit then hits a wall of detectors. We get a detection. But, the electron was never a point particle that hit the detector. Instead the wave of the electron hit one of the waves in the detector -- no points were involved.

> The singularity is also a mathematical one and not something most physicists claim exists physically.

I didn't know that, that's cool. I understand why people would say that about coordinate singularities, since it's clearly an artifact of the language and not the underlying thing, but is that also true of other kinds of singularities? I'm curious about the different schools of thought.

As a layperson, would what is beyond the edge of the (observable) universe, past the 'edge' of the expanding universe, be considered infinite? Or is that nothing / does not exist / null and void?

edit: Reading up on things (just wikipedia, bear with me), we don't know how big the universe beyond what is observable is. We can't know because we can't observe it, and what we can observe goes back ~13B years.

I think you should be careful about taking analogies too literally in physics - wave functions in basic QM are kinda like probability distributions, for instance, but they are complex valued and change when you sample from them. So they actually behave very differently.

The best way to grok the models more deeply (in my opinion anyway) is to dive into the maths!

>but they are complex valued and change when you sample from them

I see, that does sound pretty different

This is correct. Understanding is math.

My personal haha-but-serious interpretation is that we live in a simulation, which has set limits (maximums and minimums) for essentially all quantities because of the numerical methods used.

The speed of light is the maximum speed of information propagation.

Black hole event horizons are the maximum entropy per unit surface area.

Planck's constant (h) is the numerical precision ("ulp") and is the minimum representable change in the simulation state.

Etc...

  > Black hole event horizons are the maximum entropy per unit surface area.

This is an utterly fascinating way to look at it, especially in the context of your definitions of C and the Plank length.

I like to think of it as a limit imposed by the bandwidth limits between compute nodes.

A volume of computers connected in a grid with cables will have a bandwidth per unit area limit along all surfaces.

Similarly you can’t “know” about other matter in some direction away from you unless the information about it traverses the network links back towards you from there. Along a line that has a fixed upper limit. With more and more matter in some direction you get less and less information about it per unit of your time elapsing. It’s like watching a higher and higher resolution video with a fixed bandwidth — it has to play slower.

PS: hence the boundary of the visible universe is also an event horizon, it is the “depth” at which the total accumulated matter sums up to the same limit.

PS: The same line of thought works for the Anthropic principle as well! In the zoo of possible universes most have zero sentient life because the rules are not conducive to it. That’s the “core concept” but there is a nuanced version where many universes have just one species of sentient life. For example infinite travel speed would allow the first aggressive xenophobic and technically capable race to wipe out everyone else in short order. Hence, we’re more likely to be living in a universe with a speed limit where such “instant Borg assimilation” is physically impossible.

If you like to philosophise about this.. the game Eve had problems when too many players were in the same spot at the same time, and rendering everything in time.

Their solution? Time dilation..

Find your statement fascinating as well, but could also provide another haha-but-serious explanation that I personally like... which is that there are universes with an infinite permutation/computation/value of state variables, and our one could only be "simulated" within the one universe where these sort of limits exist.

It only makes sense until you realize that flow of time is literally the first thing any simulation does simulate.

There are no metaphors when dealing with the fundimentals of the universe. Metaphor is a means of teaching (ie light is a wave) but once you understand then you realize that no metaphor can ever be accurate enough. Errors occur when people see similarities between metaphors which have no meaning in the real world.

“ Kehle and Unger started with a black hole that doesn’t rotate and has no charge, and modeled what might happen if it was placed in a simplified environment called a scalar field, which assumes a background of uniformly charged particles. They then buffeted the black hole with pulses from the field to add charge to it.”

Just finished the article. Surely this can’t be the basis right? I mean everything in the universe is in motion and spins…

It did say that spinning work would require extra more complicated math but hmm. Did Hawking et al look at spinning or static black holes in 73 when they did their proof?

Imma gonna attempt to read the paper to get more context. I’m sure all the math will go way over my head tho.

> I mean everything in the universe is in motion and spins…

My understanding is that is a pretty open question as to whether or not blackholes due spin at all, or if they are all uniform apart from mass. Last I heard they do have temperature and electric charge and mass.

Another question is what does the concept of motion even mean for a singularity. How do you define the concept of distance in a non-euclidean space for an object to move through in the first place. What can the idea of movement even mean for an object that has a horizon beyond which it functionally becomes cut off from the rest of the universe.

Probably all physical black holes have some spin because they gain it from the matter that falls into it: it's conservation of angular momentum, basically. There are precise mathematical versions of rotating black holes:

https://en.wikipedia.org/wiki/Kerr_metric?wprov=sfla1

Black holes spin. (I think this is reflected in the data from LIGO about the gravitational waves from mergers?)

This spinning isn’t about the singularity spinning, but the frame dragging around the event horizon.

I took that to mean that, in theory, beginning with a scalar field, it is mathematically possible...

Not that this would be a real-life means that such a thing could come about. The "proof" they found the flaw in said a thing was mathematically impossible — they showed otherwise.

Maybe it'll help here to point out that if you start with a spinning black hole there's an easy way to stop it spinning. You just chuck in matter with the angular momentum going the opposite way to its spin until all the angular momentum has cancelled out.

Then you can do the fancy stuff from this paper with your new spinless black hole.

Can someone explain the basis for the existence of the maximum charge and maximum spin extrema? Which principles or physical phenomena enforce these limits?

I'm gonna talk about charge, essentially the same thing happens with spin, but it gets a bit more complicated.

The TLDR is this, charges with the same sign repel each other, if you're trying to make a black hole have more and more charge you have to do more and more work to push the charges you're adding into it (imagine forcing the repulsive poles of two magnets together as one of the magnets gets stronger and stronger). At an extremal black hole it is no longer possible to push hard enough to force the charge to get into the black hole.

A more interesting thing is to look at the event horizon.

First take a look a the quadratic function x^2 - a, for some positive real value a. Let's say we start at a=1, then the equation x^2 - 1 = 0 has two solutions, x=1 and x=-1, the function looks like a "u" shape passing through these points.

Now let's make a smaller and smaller, this shifts the u shape up, and the two solutions of the equation at plus or minus the square root of a get closer together. When we hit a = 0 there is only 1 solution, and when a is strictly positive there are no real solutions anymore.

Thus is roughly what happens to the event horizons of a charged black hole as you increase the charge. A charged black hole generically has two event horizons, an inner one and an outer one. As you increase the charge (while keeping the mass constant) the event horizons get closer and closer together. At the charge for an extremal black hole the two event horizons are in exactly the same place (the same as our quadratic when a=0), above this extremal charge there is no event horizon anymore.

We don't really have a good idea of what a black hole with no event horizon looks like, the event horizon of a "normal" black hole shields us from whatever insane physics is going on inside (general relativity predicts a singularity with infinite density in the middle). Most physicists believe that it is impossible for a black hole to exist with no event horizon.

Ironically completing Hawking's work to prove himself wrong. Now it's the physicists turn to prove a better mathematical model, semi-empirically.

I don't see any quantum physics involved onto that proof.

Maybe something important is missing?

I always find it funny how mathematicians try to predict real world behaviour based on some naive assumptions and some random axioms they come up.

Obviously reality slaps them in the face almost always and then they are shocked and in disbelief how their "perfect math isn't working, no this cannot be!".

I don't understand where you think that happened in this article?

The point is that hypothetically there is a way to make an extremal black hole, if you had essentially god-like powers. None of the authors are shocked or in disbelief that about this actually being possible.

In general mathematicians fall into two rough categories. Some are pure mathematicians who are happy doing their theoretical stuff and don't care whatsoever about what happens in reality. Others are more applied, and are usually very explicit about how and where their work matches and diverges from reality.

At least the way it’s described in the Quanta article, it seems like the mathematicians assumed a charged scalar field, which is not something that exists in nature. All charged particles are associated with spinor (spin 1/2) or vector (spin 1) fields. A scalar field corresponds to particles of spin 0 - the only scalar field we know of is the Higgs field, and corresponding Higgs particle is not charged. If god-like powers include a way to change the laws of physics, then your take holds up, but proving something is possible if the laws of physics were different is not very interesting.

They did their calculations with a charged scalar field essentially because this stuff is really difficult, and you want to make life as simple as you possibly can. I think there are no obvious obstructions to it working with the electron field, it's just that it would be much more involved to actually calculate everything.

Probably someday someone will do it, but I don't think it's an incredibly interesting thing to do.

So, if you have two spin (1/2) particles together, this can overall act like either a particle with spin 1 or a particle with spin 0, right?

While 4 spin (1/2) particles could either act like a particle with spin 2, or like a particle with spin 1 (in one of three different ways) or like a particle with spin 0 (5 + 3*3 + 1 = 2^4 ) right?

So, what if we consider helium-4 nuclei in the spin 0 state?

Maybe that doesn’t make sense..

> theoretical stuff and don't care whatsoever about what happens in reality.

Just an aside: I think this is an oft-repeated misconception. It’s not so much that pure mathematicians ‘don’t care about reality’ — it’s more that they consider the mathematics itself to be reality already. If mathematics isn’t reality, I’m not sure what is.

As soon as you’re doing any kind of ‘modelling’, it would be reasonable to say it’s no longer ‘pure’ mathematics. Of course, the divide between pure and applied is somewhat fuzzy.

The headline is lying.

"In 1973, the prominent physicists Stephen Hawking, John Bardeen and Brandon Carter asserted that extremal black holes can’t exist in the real world — that there is simply no plausible way that they can form. "

"The new work [...] demonstrates that there is nothing in our known laws of physics to prevent the formation of an extremal black hole."

So they didn't prove him wrong at all. Hawking asserts that it's extremely implausible for these to form, and the mathematicians said "well according to our current models technically they could !"

Shameful article. Is there a way to ask for a post to be removed ?

Imho you can outright ban quantamagazine articles while you're at it. It's hilarious that there is an intersection of tabloid press and theoretical physics, but it's also a massive waste of everyone's time.

Quanta articles are usually very good. I'm a scientist and I have been contacted by Quanta to fact-check their work before. They're very keen to make things as correct as possible.

They also don't just write articles about theoretical physics, but about pretty much anything in science and math.

They are usually terrible, with just enough sciencey-sounding content to hook non-specialists with buzzwords, and way too much unwarranted sensationalism. How many times was Einstein proven wrong this week?

They emphasise factoids with a very shallow context. Their focus on things that were proven or disproven completely hides the actual scientific work and the whole scientific method. Their headlines are most of the time garbage.

I have the same feeling about that website as I have about the Big Bang Theory: it’s too truthy not to be dangerous, and at the same time utterly wrong in all aspects that matter. Both prey on their audiences’ Dunning-Kruger tendencies.

Thats a quite surprising view to me! Thats explicitly not what the Simons foundation set them up to do.

I do agree that they are much shallower than the true scientific papers, but I would argue that that is pretty much necessary given their intended audience of non-experts. For people who want the true depth you can go and read the papers that Quanta bases their articles on, but for "normal" people I think most Quanta articles get pretty close to the optimal amount of depth you can give without completely losing the reader.

I don't agree that they overly focus on things being proven or disproven - looking at their current front page, they have one article (this one) which uses those words. The article on the Hubble tension quite sensitively describes how the various measurements we have right now disagree, and I think shows quite nicely how the scientific work in progress is going. The article on tensors is (imo) fairly boring but certainly not overly sensationalist or buzzwordy.

Basically without an example of an article that you think is really bad I don't really know what you're talking about, they're certainly not anywhere near to as bad as the big bang theory is (although I only ever watched one episode of that, so I can't talk about it properly).

To call Quanta "tabloid", even in part, is an unjustified insult for a magazine that aspires, and mostly accomplishes, to bring cutting-edge research to a larger audience (perhaps not "the masses", but still).

Personally, I cherish many articles from Quanta about areas outside my scientific expertise, and most other outlets for popular science writing are too superficial to cater for my background.

I am grateful the Simons Foundation is a supporter of Quanta Mag. - both personally because I enjoy the articles but also because tomorrow's mathematicians or scientists may be motivated/inspired by their material.

I do not believe in charity. This is another datum to add to the list. Don't care about no Simons Foundation. Just don't like the clickbait of quantamagazine. Never got anything out of any of their articles, would much prefer if the original papers got posted here. But I see people like their cheesy science news.

I think posting the original papers here would generally not be useful. I am a scientist, specifically in quantum information theory and I can't read scientific papers in other fields without a significant amount of time and effort. If you show me a paper in cosmology or virology or number theory I'm generally not going to be able to follow it (unless I put in a decent amount of time studying the stuff it's based on).

I think the same is true of almost everyone on this website (maybe we have a couple of polymaths around). Popular science like quanta performs a useful service in making stuff which would otherwise be somewhat inaccessible to me, much much less so.

We're not complaining about making papers more accessible, but about the clickbait and the resulting misrepresentation.

I was responding to

> would much prefer if the original papers got posted here

I don't think this would generally be useful.

Can you provide an example of a Quanta article you found particularly misrepresentative? I haven't read many of their articles, but the ones I have read seemed pretty decent. They also once asked me to fact-check one of their articles and I was quite impressed with how keen they were to get the science right. Not only did they ask me to read the article and provide any feedback (which is what I expected), but they came with a list of the parts where they were concerned they might have misunderstood something.

The headline is not lying. Bekenstein, Hawking, Bardeen and Carter asserted four laws of black-hole thermodynamics and proved three of them. The fourth is what the guys this article is about proved is wrong.

The sentence with the word plausible is a bit deceptive, but the headline is fine.

Reply on news.ycombinator.com