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Mathematicians prove Hawking wrong about the most extreme black holes

148 points by worldvoyageur 2y ago

Xen9 2y ago
Ironically completing Hawking's work to prove himself wrong. Now it's the physicists turn to prove a better mathematical model, semi-empirically.
worldvoyageur 2y ago
" 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 2y ago
  >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 2y ago
    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 2y ago
      But it would not be falling into "nothing". There is an accretion disc.
      - ben_w 2y ago
        There can be an accretion disc, but it's not a necessary property for a black hole to have.
        mystified5016 2y ago
        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.
        floxy 2y ago
        Tidal forces at the event horizon of supermassive black holes are negligible. https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf
      - observationist 2y ago
        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 2y ago
  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 2y ago
    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 2y ago
    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.
    - mr_toad 2y ago
      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.
- chasil 2y ago
  "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 2y ago
    > Three properties completely describe a black hole: mass, spin, and charge. So it's like an elementary particle?
    - chasil 2y ago
      I think the precursor neutron star might be closer.
      - The_Colonel 2y ago
        Neutron star is still composed of... neutrons. There is a hypothesised Quark star though.
        graycat 2y ago
        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.
- mr_toad 2y ago
  > 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.
Vecr 2y ago
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 2y ago
>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 2y ago
  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 2y ago
  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.
gigatexal 2y ago
“ 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 2y ago
  > 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 2y ago
    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 https://en.wikipedia.org/wiki/Kerr_metric?wprov=sfla1
  - drdeca 2y ago
    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.
- 2y ago
Jean-Papoulos 2y ago
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 2y ago
  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 2y ago
    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 2y ago
      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.
NotGMan 2y ago
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 2y ago
  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 2y ago
    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.
    - eigenket 2y ago
      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.
schoen 2y ago
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 2y ago
  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.
notorandit 2y ago
I don't see any quantum physics involved onto that proof. Maybe something important is missing?

148 points by worldvoyageur 2y ago

Xen9 2y ago

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

worldvoyageur 2y ago

" 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 2y ago
>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 2y ago
  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 2y ago
    But it would not be falling into "nothing". There is an accretion disc.
    - ben_w 2y ago
      There can be an accretion disc, but it's not a necessary property for a black hole to have.
      - mystified5016 2y ago
        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.
        floxy 2y ago
        Tidal forces at the event horizon of supermassive black holes are negligible. https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf
    - observationist 2y ago
      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 2y ago
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 2y ago
  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 2y ago
  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.
  - mr_toad 2y ago
    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.
chasil 2y ago
"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 2y ago
  > Three properties completely describe a black hole: mass, spin, and charge. So it's like an elementary particle?
  - chasil 2y ago
    I think the precursor neutron star might be closer.
    - The_Colonel 2y ago
      Neutron star is still composed of... neutrons. There is a hypothesised Quark star though.
      - graycat 2y ago
        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.
mr_toad 2y ago
> 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.

Vecr 2y ago

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 2y ago

>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 2y ago
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 2y ago
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.

gigatexal 2y ago

“ 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 2y ago
> 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 2y ago
  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 https://en.wikipedia.org/wiki/Kerr_metric?wprov=sfla1
- drdeca 2y ago
  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.
2y ago

Jean-Papoulos 2y ago

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 2y ago
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 2y ago
  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 2y ago
    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.

NotGMan 2y ago

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 2y ago
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 2y ago
  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.
  - eigenket 2y ago
    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.

schoen 2y ago

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 2y ago
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.

notorandit 2y ago

I don't see any quantum physics involved onto that proof. Maybe something important is missing?