[HN Gopher] Mathematicians prove Hawking wrong about the most ex...
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Mathematicians prove Hawking wrong about the most extreme black
holes
Author : worldvoyageur
Score : 130 points
Date : 2024-08-21 14:50 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| worldvoyageur wrote:
| " 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?
| floxy wrote:
| >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.
| observationist wrote:
| 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.
| dotancohen wrote:
| But it would not be falling into "nothing". There is an
| accretion disc.
| ben_w wrote:
| There _can be_ an accretion disc, but it 's not a
| necessary property for a black hole to have.
| observationist wrote:
| 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.
| bobbylarrybobby wrote:
| 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.
| marcosdumay wrote:
| It's a bit of a contradiction with the idea of a black hole,
| and brings the feature that you can observe its surface.
| dotancohen wrote:
| 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.
| chasil wrote:
| "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?
| zvrba wrote:
| > Three properties completely describe a black hole: mass,
| spin, and charge.
|
| So it's like an elementary particle?
| chasil wrote:
| I think the precursor neutron star might be closer.
| Vecr wrote:
| 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.
| ackbar03 wrote:
| >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
| e1gen-v wrote:
| 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.
| meroes wrote:
| 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.
| ackbar03 wrote:
| 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.
| untilted wrote:
| 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/equi
| valen...
| 6gvONxR4sf7o wrote:
| > 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.
| bubblyworld wrote:
| 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!
| ackbar03 wrote:
| >but they are complex valued and change when you sample from
| them
|
| I see, that does sound pretty different
| kansface wrote:
| This is correct. Understanding is math.
| jiggawatts wrote:
| 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...
| dotancohen wrote:
| > 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.
| moi2388 wrote:
| 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..
| songeater wrote:
| 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.
| scotty79 wrote:
| It only makes sense until you realize that flow of time is
| literally the first thing any simulation does simulate.
| sandworm101 wrote:
| 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.
| gigatexal wrote:
| " 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.
| gustavus wrote:
| > 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.
| roywiggins wrote:
| 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
| drdeca wrote:
| 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.
| JKCalhoun wrote:
| 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.
| eigenket wrote:
| 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.
| Jean-Papoulos wrote:
| 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
| ?
| jona-f wrote:
| 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.
| eigenket wrote:
| 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.
| kergonath wrote:
| 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.
| eigenket wrote:
| 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).
| jll29 wrote:
| 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.
| eigenket wrote:
| 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.
| NotGMan wrote:
| 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!".
| eigenket wrote:
| 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.
| om2 wrote:
| 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.
| schoen wrote:
| Can someone explain the basis for the existence of the maximum
| charge and maximum spin extrema? Which principles or physical
| phenomena enforce these limits?
| eigenket wrote:
| 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.
| Xen9 wrote:
| Ironically completing Hawking's work to prove himself wrong. Now
| it's the physicists turn to prove a better mathematical model,
| semi-empirically.
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