[HN Gopher] Black holes finally proven mathematically stable
       ___________________________________________________________________
        
       Black holes finally proven mathematically stable
        
       Author : shantanu_sharma
       Score  : 167 points
       Date   : 2022-08-04 14:28 UTC (8 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | lowpro wrote:
       | General question: where does this research lead to? As in what
       | might be the next step for this research team, and/or their field
       | in general? I always like to understand what discoveries like
       | this could open up in the future.
       | 
       | *Asking as someone not in the field or any type of
       | physics/mathematics
        
       | ziddoap wrote:
       | > _In a 912-page paper posted online on May 30, Szeftel, Elena
       | Giorgi of Columbia University and Sergiu Klainerman of Princeton
       | University have proved that slowly rotating Kerr black holes are
       | indeed stable._
       | 
       | I wouldn't have expected it to be a short paper, but... 912
       | pages!
       | 
       | While I'm not a cosmologist, I usually enjoy reading through the
       | papers that pop up. I think I might end up skipping this one and
       | just stick to the Quanta article, unfortunately.
       | 
       | Hopefully Anton Petrov does a summary video on the paper.
        
         | Victerius wrote:
         | PHYS 540 General Relativity
         | 
         | Homework problem of the week: Prove that slowly rotating Kerr
         | black holes are stable.
         | 
         | Deadline: Two weeks.
         | 
         | Final grade weight: 5%
        
           | sidlls wrote:
           | You joke, but I recall my graduate level GR class homework.
           | Just mechanically writing out solutions (the GR equivalent to
           | writing the correct integral down and then evaluating it) to
           | a much less exciting problem, starting with the most basic
           | mathematical representation of the tensor field(s) involved
           | would take pages and pages of handwritten work. It's a
           | fascinating field.
        
           | dylan604 wrote:
           | The assignment website to upload work keeps telling me that
           | my upload is too big. It says there's a 900 page limit
        
             | lapetitejort wrote:
             | "Just... cut a few."
             | 
             | "Which pages do you have in mind, professor?"
        
               | dylan604 wrote:
               | the one with the final answer of course. you get majority
               | of credit from showing your work
        
         | curt15 wrote:
         | The original proof of the stability of Minkowski spacetime was
         | too long for a paper, so the authors wrote a 500 page book:
         | https://press.princeton.edu/books/hardcover/9780691632551/th...
        
         | V__ wrote:
         | > an 800-page paper by Klainerman and Szeftel from 2021, plus
         | three background papers that established various mathematical
         | tools -- totals roughly 2,100 pages in all.
         | 
         | It basically comes in three volumes. What an astonishing amount
         | of work.
        
         | rrishi wrote:
         | At 912 pages, thats a book not a paper (i jest)
        
           | samstave wrote:
           | The Tome of The Black Hole's Mathematical Stability was so
           | massive, at 912 pages, hardly a word in the English language
           | escapes the horizon of events unfolding betwixt its covers.
        
           | varjag wrote:
           | Oh come on. You'd often get that much for an MCU part and
           | they call it a (data)sheet.
        
           | sharkweek wrote:
           | > (i jest)
           | 
           | Infinite Jest? 70 pages longer (if you don't include the
           | footnotes)
        
             | rrishi wrote:
             | i meant that i was kidding calling it a book.
        
               | baq wrote:
               | at 2100 pages it's a trilogy, so yeah...
        
         | WebbWeaver wrote:
         | I'm definitely going to go in there and find out how they
         | defined 'slowly rotating.' I bet its pretty cool.
        
           | walnutclosefarm wrote:
           | The Quanta overview basically answered this - they consider
           | the ration of the black hole's angular momentum to its mass.
           | A "slow" black hole is one where this ratio is much less than
           | one. How much less than one it has to be, the paper's authors
           | apparently don't derive.
        
         | codethief wrote:
         | > While I'm not a cosmologist
         | 
         | The people behind the above prove and similar works do research
         | relatively far away from cosmology, in a field usually called
         | mathematical General Relativity. In particular, they are
         | usually mathematicians by training, not physicists.
         | 
         | Sad side note: Most physicists (even many of those doing
         | research in General Relativity) have never heard of
         | mathematical GR.
        
           | ziddoap wrote:
           | My understanding is that GR forms the basis of the discipline
           | of cosmology, but your comment implies it doesn't. Could you
           | expand on that a bit? What differentiates GR and
           | 'mathematical GR'? Why is the formation/stability of
           | blackholes not considered to be a part of cosmology, when the
           | understanding of black holes is central to understanding how
           | to universe formed?
           | 
           | e.g. "General Relativity forms the basis for the disciplines
           | of cosmology (the structure and origin of the Universe on the
           | largest scales) and relativistic astrophysics (the study of
           | galaxies, quasars, neutron stars, etc.)"
           | 
           | from https://uwaterloo.ca/applied-mathematics/future-
           | undergraduat...
        
             | layer8 wrote:
             | _A_ forming the basis of _B_ doesn't imply that everyone
             | working on _A_ will be considered a _B_ -ologist.
        
               | ziddoap wrote:
               | Sure, I get that, but parent said:
               | 
               | > _relatively far away from cosmology_
               | 
               | and that surprised me, because it doesn't seem that far
               | away in my eyes. Which is why I was genuinely asking for
               | clarification. They might not be cosmologists, but this
               | paper seems pretty close to cosmology, not 'far away'
               | from it.
               | 
               | If it's not, I'm happy to be wrong, but I'd like to be
               | corrected rather than just told I'm wrong.
        
       | vishnugupta wrote:
       | > In a 912-page paper
       | 
       | I don't envy peer reviewers.
        
       | woopwoop wrote:
       | Oh man, 912 pages, they almost beat Almgren's big regularity
       | paper.
        
       | googlryas wrote:
       | The result of 900 pages of math:
       | 
       | Q(A) = 1 2 (c)D[?]b (c)DPq + r -4 /d <=1 (Gb, rGg) + O(ar-3 )d
       | <=1B + O(ar-4 )A + O(ar-3 )d <=1Pq +r -1 d <=1 (Gb * (P , B q ))
       | + r -2 d <=1 (Gg * (rB, A)) + Ks[?]b (c)[?]3B + r -1 d <=1 (Ks *
       | A),
        
         | dalbasal wrote:
         | Terrific, but terrifying.
        
           | dylan604 wrote:
           | My cat is a genius, as I swear that's what he typed after
           | walking across my desk a couple of times with a text editor
           | window having focus
        
           | mixmastamyk wrote:
           | Breaking it down into a series of operations would help a
           | lot. perl-esque obfuscated one-liners are just that.
        
       | lokimedes wrote:
       | Karl Popper would have been sent spinning at a headline like
       | that. Our knowledge of Black holes as physical objects is hardly
       | affected by someone mathematically "proving" that a mathematical
       | model is consistent. Only empirical observations/experiments can
       | change physical fact. This confusion of mathematics with physics
       | is not helping us understand the Universe as it really is. At
       | most, this many lead to a prediction that may be falsified, but
       | we kinda had the "stability of black holes" on the todo list
       | already.
       | 
       | I know people who stare at protons to see if they really are
       | stable. Current lifetime is around 1e39 years or something...
       | 
       | Now I'm ranting on (sorry, this is bad HN etiquette), I both
       | enjoy and regret the seemingly reverence of the physical "laws"
       | by non-physicists. Applicability is not equal to universality,
       | great mathematical models of physical phenomena such as
       | Electromagnetism, General Relativity and the whole Quantum Field
       | Complex, are testaments to the human imagination and
       | resourcefulness, but they are just someone's mathematical
       | representation of an idea about how the universe act. We should
       | be more aggressively prodding at the weak points of these models
       | but also seek to explore novel representations of the same
       | phenomena with the hope of new predictive power from changing the
       | basis. I also hoped for more "general searches" and robotic
       | experimentation to allow experiments without the "bias" of the
       | theorists imagination to influence the way we look for new
       | physics.
        
         | chowells wrote:
         | Didn't this paper _exactly_ prod a model 's weak point until
         | they eventually determined the model was consistent with the
         | observed universe? Isn't that exactly what you're asking for?
        
       | jstogin wrote:
       | I see a number of people commenting on the size of the proof
       | (roughly 900 pages) which is not uncommon in this particular sub-
       | field of PDEs. For context, I had the distinct privilege of
       | studying under Sergiu Klainerman for my PhD on this topic. My own
       | dissertation was about 600 pages. From my personal experience, I
       | have come to understand a few factors that contribute to large
       | proof sizes. 1. A lot of work is on inequalities involving
       | integrals with many terms. These are difficult to express without
       | taking up substantial space on the page. Some inequality
       | derivations themselves might take multiple pages if you want to
       | go step-by-step to illustrate how they are done. 2. Writing a
       | proof of this size is not unlike building a medium-to-large size
       | codebase. You have a lot of Theorems/Classes that need to fit
       | together, and by employing some form of separation of concerns
       | you can end up with something quite large and complex. 3.
       | Verifying this kind of proof isn't usually done all at once. A
       | lot of verification happens on the individual lemmas before
       | they're pieced together. Once the entire paper is written,
       | verification is more of a process where you rely on intuition for
       | what the "hard parts" of the proof are and drilling down on
       | those. But when writing the paper, you must of course account for
       | all the details regardless of whether they are "easy" or "hard",
       | and there can be many.
       | 
       | Having said all this, I have not read their paper and it has been
       | 5 years since I was in this space. This is a truly remarkable
       | accomplishment and the result of decades of hard work!
       | 
       | I'll end with an amusing anecdote. A fellow grad student, when
       | deciding between U of Chicago and Princeton for his PhD program
       | was pitched by a U of Chicago professor who once said something
       | like "Of course you could go to Princeton and write 700 page
       | papers that nobody reads." When this story was shared during a
       | conversation over tea at Princeton, another professor retorted,
       | "Or you could have gone to U Chicago to work with him and write
       | 70 page papers that nobody reads!"
        
         | arcen wrote:
         | Are there any tools that are used to manage all the pieces?
        
         | auntienomen wrote:
         | How do you know you don't have errors in a 600 page proof?
        
         | swayvil wrote:
         | Would it be possible to create a proof of a proof?
         | 
         | Like : Given this list of assumptions -- This list of
         | conclusions is proven to be true.
         | 
         | Maybe even with a confidence rating.
         | 
         | Then you could package your proof inside the proofproof. Thus
         | sparing us the effort of reading it, and maybe even make your
         | proof more widely appreciated.
        
           | Archelaos wrote:
           | > Would it be possible to create a proof of a proof?
           | 
           | The sub-discipline of mathematics that deals with this is
           | called "metamathematics". For a start see
           | https://en.wikipedia.org/wiki/Metamathematics
        
           | mensetmanusman wrote:
           | Sounds like the halting problem :)
        
           | thomasahle wrote:
           | In principle you could provide what's called a
           | Probabilistically Checkable Proof. This would be a long
           | string of bits, and a verifier would only have to sample 3
           | random bits to check the validity of the whole thing.
           | 
           | In practice we don't even make "normal" machine checkable
           | proofs. They are just too much work. Maybe in the future when
           | the machines are better at understanding us.
        
         | gigatexal wrote:
         | What an insane effort. And to think the peers of these folks
         | that had to edit/accept this stuff had to check and verify the
         | new math they came up with for the proof.
         | 
         | That's my one issue -- is it dubious we have to come up with
         | new math to prove stuff? Or is that readable especially when
         | dealing with such exotic things like black holes?
        
         | momentoftop wrote:
         | If the proof is that size, I'd leave it out of my thesis
         | proper, and just provide a link to it as a stable artifact.
        
         | whatshisface wrote:
         | Can anyone build on results that are so hard-won and complex
         | that understanding them is as much effort as learning the
         | basics of some entire fields of study?
        
           | LeifCarrotson wrote:
           | Yes. That's how basically all expansion to the field of human
           | knowledge is constructed today.
           | 
           | A human can only ingest and understand so much information in
           | so much time. As Matt Might[1] eloquently described in "The
           | Illustrated Guide to a PhD" [2], learning the basics of an
           | entire field of study is what a bachelor's degree is for, a
           | master's degree gives you a specialty, graduate students
           | reading research papers like this one is how you get to the
           | edge of human knowledge...only then can you start building on
           | that sum of knowledge.
           | 
           | [1] http://matt.might.net/
           | 
           | [2] http://matt.might.net/articles/phd-school-in-pictures/
        
             | btrettel wrote:
             | I don't agree with that article. I previously wrote about
             | my disagreement on HN:
             | https://news.ycombinator.com/item?id=29141107
             | 
             | To summarize, a PhD often (maybe even typically) does not
             | bring someone to the edge of human knowledge. Often a PhD
             | gets people near it, but given the shear amount of
             | scientific literature out there, it's difficult to know
             | where the edge is.
        
           | jstogin wrote:
           | Some graduate students will likely spend a substantial part
           | of their PhD understanding this paper. They will learn a lot
           | in the process, and then they can contribute by either
           | extending the result or finding a way to simplify a part of
           | the proof. Or if they have a (very) related interest, they
           | may be able to adapt some of the techniques to the problem
           | they're interested in. Slowly over time, through this
           | process, the knowledge might diffuse to other less related
           | areas.
        
           | cercatrova wrote:
           | Oftentimes proofs start out very complex but become simpler
           | as time goes on and more people understand it and connect it
           | to other existing ideas.
           | 
           | It is akin to refactoring a codebase after it started as a
           | spaghetti code behemoth.
        
         | markmiro wrote:
         | If these proofs really are like codebases, wouldn't we
         | eventually expect these proofs to be written as software?
         | 
         | You'd install lemmas using a package manager and then import
         | them into your proof.
         | 
         | You can then install updates to proofs. Maybe someone has found
         | the proof to be wrong, in which case you either find a
         | different proof or invalidate the lemma so all the dependents
         | can be invalidated automatically.
        
           | HighlandSpring wrote:
           | And the individual lemmas could have author and chronology
           | metadata attached, then you could plot the DAG as a
           | roadmap/tech tree of sorts with an axis corresponding to
           | time.
           | 
           | You'd be able to at a glance see the year a result entered
           | public domain, who authored it, etc
           | 
           | One can dream
        
       | TobTobXX wrote:
       | Somewhat OT, but I've had this question for a while now: Why do
       | we know that black holes have a singularity? This might be a dumb
       | question, but when you increase the mass of, let's say, a neutron
       | star, at some point gravitaton is too strong for light to escape
       | and there'll be a Schwarzschild border. But why does the mass
       | inside of a black hole have to shrink to a singularity? Can't
       | there be some ultra-dense but finitely small core?
        
         | gizmo686 wrote:
         | If we assume general relativity is correct, then singularities
         | are an unavoidable result of black holes. The math simply does
         | not allow for such a large density to not form a singularity.
         | Having said that, we know GR is not correct, as it fails to
         | account for any quantum phenomena; and we have thus far been
         | unable to combine GR and QFT into a unified theory. Attempts to
         | combine the theories fall under the title of quantum gravity.
         | Several proposed theories of quantum gravity predict that black
         | hole singularities do not exist.
        
         | pixl97 wrote:
         | Essentially the Schwarzschild equations based off relativity
         | say that happens.
         | 
         | The problem turns out that we have no way to actually know if
         | that's what happens at the core of the black hole. The event
         | horizon presents a problem where it becomes impossible to
         | experimentally test anything beyond that point. For example the
         | fundamental constants could alter themselves inside the event
         | horizon, as long as the event horizon was still a one way trip,
         | it wouldn't matter, we'd not be able to gather any information
         | about that.
        
         | starwind wrote:
         | As I understand it: before gravity captures light--which moves
         | as fast as anything can move--gravity will have captured
         | everything else and overcame all other repulsive forces
         | crushing the matter into a singularity
         | 
         | edit: pixl97 made a really good point right as I posted. I
         | should say "As I understand _the math_ "
        
         | pas wrote:
         | I'm not familiar with the current thinking about this, but last
         | decade the singularity was understood as a gap in our
         | understanding/model. Of course there's model dependent realism,
         | after all if all you have are models (built on decades or
         | centuries of data), with no means of devising new experiments,
         | what else is reality?
        
       | jmyeet wrote:
       | I'm can't help but imagining a world where the papers on black
       | holes become so large they themselves undergo gravitational
       | collapse and become black holes.
       | 
       | Exercise for the reader: how large can a paper get before
       | collapsing?
       | 
       | Seriously though, can someone comment on this and it's
       | significance?
        
         | drexlspivey wrote:
         | It is known that if you manage to fold a paper in half more
         | than 7 times it becomes a black hole
        
         | codethief wrote:
         | > Seriously though, can someone comment on this and it's
         | significance?
         | 
         | I have not been part of the hyperbolic PDE subfield of
         | mathematical relativity (but a sibling subfield) but the
         | (in-)stability of Kerr black holes had always been presented to
         | me as one of the big open questions in that field.
         | 
         | And, now putting on my physicist's hat, it is indeed: I mean,
         | if Kerr black holes had turned out to be instable, then black
         | holes wouldn't last very long and the question would have been
         | what the photos from the Event Horizon Telescope are actually
         | showing. (Note: It is expected that in nature all black roles
         | rotate at least slightly, so are of the Kerr kind.)
        
         | antognini wrote:
         | As someone who has done a PhD in gravitational dynamics I think
         | I can say that there are probably only a few dozen people in
         | the world who can comment intelligently on this paper.
        
           | lisper wrote:
           | What happens when those few dozen people die?
        
             | strbean wrote:
             | Then we have to make more.
        
         | a1369209993 wrote:
         | > how large can a paper get before collapsing?
         | 
         | Assuming it's confined to a one meter radius, the Bekenstein-
         | Schwarzschild limit comes out to around `(1m)^2 (tau c^3 log(e)
         | / 2hbar G)` or about 2^230 bytes (or 2^150 yottabytes, at the
         | point where SI prefixes run out).
         | 
         | If you're limited to storing one bit per amu (or other unit of
         | mass), rather than saturating the Bekenstein bound for your
         | space-energy budget, you only really care about the
         | Schwarzschild limit (`(1m) c^2 / 2 G * (1bit/amu)`), which
         | gives 2^175 bytes or 2^95 yottabytes.
         | 
         | Obviously, if you have more space available, there's no hard
         | upper bound, although you may need to put some parts of the
         | (physical storage substrate of the) paper into orbit around
         | other parts to keep the mass density below the (decreasing with
         | radius) density of a black hole of that radius.
        
       | frakt0x90 wrote:
       | Is this more than a preprint? Usually really long research like
       | this takes a long time to verify, like that guy who claimed to
       | solve the abc conjecture. The article talks about it like
       | everyone agrees this is valid, but is it?
        
         | YetAnotherNick wrote:
         | Paper was posted on 30th May and this article was written on
         | 4th August. So it is possible it has been verified.
        
           | gus_massa wrote:
           | That's only 2 months for 900 pages, like 15 pages per day,
           | it's impossible to read it so fast. IIRC checking the proof
           | of the last Fermat theorem took a few years (and a few
           | modifications to fix holes).
        
         | corndoge wrote:
         | FTA:
         | 
         | > [...] He did stress, however, that the new paper has not yet
         | undergone peer review.
        
         | woopwoop wrote:
         | Probably there isn't anyone who wasn't an author who can vouch
         | for it yet, but this is a different situation. These guys have
         | been working toward this problem for a long time in much closer
         | touch with the mathematical community, with partial results
         | that people can vouch for. This contrasts with the situation
         | with the abc conjecture, which was done in almost complete
         | isolation from the mathematical community with as far as I know
         | no intermediate results.
        
       | primitivesuave wrote:
       | > Klainerman emphasized that he and his colleagues have built on
       | the work of others. "There have been four serious attempts," he
       | said, "and we happen to be the lucky ones." He considers the
       | latest paper a collective achievement, and he'd like the new
       | contribution to be viewed as "a triumph for the whole field."
       | 
       | Come what may in peer review, this is an admirable attitude to
       | have toward science.
        
       | lotw_dot_site wrote:
       | At a certain point of abstraction, theoretical physics almost
       | never has any direct correlation with empirical reality. It is
       | most often used as a way to give the paradigm lenses that color
       | our thoughts nice little workouts. (One can also apply
       | Wittgenstein's notion of language games here.)
       | 
       | If, by the term "black hole", a person is referring to some
       | object that has the shape of a mathematical point, then it just
       | doesn't make much sense to call it a thing that relates to the
       | world of observation. (The postulates of Quantum Mechanics
       | dictate that physical objects _must_ be fundamentally spread out
       | in the form of wave functions.)
       | 
       | Solutions to simplistic kinds of mathematics come in the form of
       | idealizations called "points". But physical reality is
       | fundamentally spatial, and the necessary maths must involve
       | things like topological manifolds, which brings us directly to
       | the doorstep of String Theory, which is not so much a "theory"
       | but rather a broad category that consists of the entire spectrum
       | of all possible Quantum Field Theories. String Theorists, in
       | fact, are always speculating over the possibility of some given
       | theory's existence, such as when Witten spoke of a mysterious
       | "M-theory" in the mid-90's.
        
         | colechristensen wrote:
         | What? Lighten up on the philosophy of a topic before you
         | understand it.
         | 
         | Sure, the physical reality of the singularity is a bit of a
         | mystery as it comes up against the nature of gravity at an
         | extreme which requires a quantum theory which includes general
         | relativity, but that is a known unknown and not what any of
         | this black hole physics is about.
         | 
         | Outside of the singularity, and definitely outside the event
         | horizon, a black hole is a very real thing which has been seen
         | and measured in "empirical reality" and theory has so far
         | matched well with measurement.
         | 
         | Nobody is going to Euclid and claiming a point or line is a
         | real physical entity, anything but a useful abstraction.
        
           | lotw_dot_site wrote:
           | >Lighten up on the philosophy of a topic before you
           | understand it
           | 
           | But philosophy is an activity that must necessarily be done
           | in order for there to even _be_ a topic that can at all be
           | understood in the first place! We had to have someone like
           | Descartes before we could get someone like Newton, and Newton
           | before the quantum theorists, etc.
           | 
           | The idea that you can just jump straight to (and always stay
           | within the framework of) "hard science" and do away with the
           | malleable philosophical bits that allow for the kind of
           | connective tissue that binds civlizations is perhaps the
           | biggest reason why we collectively face the existential
           | crises that we currently do.
           | 
           | And the other idea that everyone (or at least everyone who
           | has jumped through the hoops to get the necessary
           | credentials) can simply sit fat and happy in their own arcane
           | specialties as long as they are able to "prove" their worth
           | to the rest of us by patting each other on the back with
           | their circles of academic citations is... well... not very
           | sustainable. All academic disciplines, to the extent that
           | they cannot remain "rooted" within some larger framework of
           | philosophical sensibility will necessarily get weeded in due
           | time.
        
             | colechristensen wrote:
             | No, this isn't about the philosophy of science, but you in
             | particular misrepresenting a topic and then making
             | philosophical arguments about it. You ought to understand
             | the science you're criticizing before sharing your
             | commentary on it.
        
         | whatshisface wrote:
         | > _a person is referring to some object that has the shape of a
         | mathematical point_
         | 
         | Black holes aren't points, they're space-time shapes with a
         | singularity at the middle and a spherical event horizon. The
         | black hole at the center of our galaxy extends across 16
         | million miles, or a little over eighteen times the size of our
         | sun.
         | 
         | If the singularity at the middle is slightly modified to be
         | something else according to a better theory of gravity (most
         | physicists believe that this will eventually happen), the
         | outlying spacetime will not change very much, for reasons
         | similar to how Newton was able to work out how the planets
         | moved around the sun without knowing what the sun was made of
         | or what was inside it.
         | 
         | If you imagine a circus tent propped up in the middle by a
         | square pole, it will look very much like one propped up by a
         | round pole. That's because solutions to the Laplace equation
         | smooth themselves out as quickly as possible as you move away
         | from the boundary condition.
        
           | otikik wrote:
           | I thought wether or not a singularity sits at the center of a
           | black hole is actively discussed.
           | 
           | Or to be more precise: our math seems to indicate that there
           | is one ... _and precisely because of that we think that our
           | math might be wrong or incomplete_ (because every single time
           | we have encountered an  "infinite" or something resembling
           | that in the past it turned to be an error).
        
             | colechristensen wrote:
             | General Relativity says there is a singularity, more than
             | one depending on the metric and coordinate system chosen.
             | 
             | However GR is not a quantum theory and it is well known
             | that it clashes with quantum mechanics in ways that would
             | show up in a singularity so what the physical reality of
             | space actually at and nearby the singularity is still a
             | mystery because we don't yet have an accepted theory of
             | quantum gravity.
        
               | lisper wrote:
               | [deleted because brain wedgie]
        
               | colechristensen wrote:
               | That's literally the rest of my comment.
        
               | lisper wrote:
               | Sorry about that.
        
             | [deleted]
        
           | lotw_dot_site wrote:
           | >they're space-time shapes with a singularity at the middle
           | 
           | Upon googling "black hole singularity", the first "People
           | also ask" is "Does black hole contain singularity" and the
           | answer is, "No, black holes in our universe, that is to say
           | the real universe, do not contain singularities." While this
           | doesn't in itself invalidate your point, it does seem to
           | raise questions.
           | 
           | >The black hole at the center of our galaxy extends across 16
           | million miles, or a little over eighteen times the size of
           | our sun.
           | 
           | I think what you are doing here is conflating the physical
           | effects of the thing (the gravitational field of force) with
           | the mathematical description of the thing itself (a precisely
           | defined geometric structure). If you are talking about
           | extremely strong gravity fields, such as those that bind
           | entire galaxies (or galaxy clusters or even larger
           | organizational patterns), then that is one class of things
           | (empirical), but the purely theoretical notion of physical
           | singularities is an entirely different class of things
           | altogether (a class, which, IMO is perfectly self-
           | contradictory).
           | 
           | >That's because solutions to the Laplace equation smooth
           | themselves out as quickly as possible as you move away from
           | the boundary condition.
           | 
           | This seems incorrect. I find that solutions to the Laplace
           | equation typically "smooth themselves out" in a quasi-linear
           | way (ie, the way sines and cosines do). The most vexing
           | question in Quantum Mechanics is in fact why quantum states
           | (i.e. the eigenfunctions that are solutions to PDE's such as
           | Laplace's equation) appear to us as localized packets rather
           | than how their "wave functional" mathematical descriptions
           | would dictate (diffuse). The way this conundrum is resolved
           | in QM is by way of a perfectly ad-hoc procedure called
           | "collapsing the wave function".
        
       | sethjr5rtfgh wrote:
       | They're stable if you put them in a box.
        
       | hamiltonians wrote:
       | how do you even check 900 pages of dense hard math...nuts. goes
       | to show how top math and physics people in whole other leauge
       | compared to college level
        
         | spicymaki wrote:
         | I had the same question. Who could even review this for
         | correctness?
        
         | EGreg wrote:
         | Is this all humans or computer stuff?
        
           | woweoe wrote:
           | The agreement between the UK and EU ran to 1250 pages in
           | English alone.
        
           | untilted wrote:
           | check for yourself: https://arxiv.org/pdf/2205.14808.pdf
        
       | NHQ wrote:
       | Great, let us see our own black hole with the James Webb, it
       | should be relative to a mirror.
        
       | spicymaki wrote:
       | Perhaps it is getting a bit ridiculous publishing 900+ pages of a
       | math proof in a pdf format. Perhaps mathematicians should move to
       | a GitHub style publication platform.
        
         | _Microft wrote:
         | For a paper, I would take a PDF over basically any other form
         | of media any day of the week. Being able to archive a paper
         | easily and print it in the form as the author intended it is
         | extremely valuable.
        
           | dalbasal wrote:
           | Yes, if you want to print it out on paper... but don't you
           | think someone might want machine readable?
        
             | lmkg wrote:
             | We don't have a good way to handle equations. They are
             | dense and sometimes minute aspects of positioning have
             | semantic value. And this paper in particular, the equations
             | are the core of the content.
             | 
             | There's room for improvement over the status quo, but with
             | the standards we have available today, faithfully
             | representing the content requires a faithful representation
             | of the visual layout. So a typesetting format like PDF is
             | what's needed.
        
               | gjs278 wrote:
        
               | lisper wrote:
               | > We don't have a good way to handle equations.
               | 
               | S-expressions?
        
               | strbean wrote:
               | > We don't have a good way to handle equations.
               | 
               | LaTeX?
        
               | gus_massa wrote:
               | Looking behind the curtain (i.e. .tex files) is a
               | horrible experience.
               | 
               | You expect to see
               | 
               | $a^2+b^2=c^2$
               | 
               | but you actually see manually spacing, sub/super-index
               | before and after the object, weird hats, ...
               | 
               | $a+{}^2\\!\hat{x}\ \leq& \ 7\ y_2\\!\\!^5+\epsilon$
        
             | archgoon wrote:
             | Pdfs are readable by machines. It's also released as tex.
             | 
             | https://arxiv.org/format/2205.14808
             | 
             | Huh. this account apparently got shadowbanned. Guess it's
             | another good reminder not to post here.
        
               | CBarkleyU wrote:
               | I guess I can see you from the shadows...
        
               | _Microft wrote:
               | If you think that something is wrong with your account,
               | you can get in touch with the moderators via the
               | "Contact" link in the footer of the page.
        
               | archgoon wrote:
        
             | xyzzyz wrote:
             | Do you know what physicists or mathematicians actually
             | want, or are you just theorizing as an outsider, based on
             | experience from completely different domain?
        
               | Loughla wrote:
               | I'm confused by the reason behind your question (which
               | I'm assuming you have, I guess). Are you arguing that
               | scientific works shouldn't be made accessible?
        
               | panda-giddiness wrote:
               | Unless you are a physicist or mathematician, I doubt any
               | format will make this work "accessible".
        
               | Loughla wrote:
               | I think maybe we have a difference in what accessible
               | means. I'm talking accessible as in, 'I can literally
               | access this', not as in 'I can understand what this
               | means'.
               | 
               | I use a screen reader, and unless the pdf is explicitly
               | created as an accessible pdf, it is just garbled up
               | nonsense.
        
               | xyzzyz wrote:
               | If you cannot read the PDF, you can also download LaTeX
               | source from arxiv. I don't think it is reasonable to
               | expect anything more accessible than that.
        
               | simonh wrote:
               | If PDF format is the preferred format of those needing to
               | access the work, compared to likely alternatives, then it
               | is accessible. Are you claiming you know better what the
               | needs of professionals in the field are?
        
               | gjs278 wrote:
        
               | Loughla wrote:
               | I think maybe we have a difference in what accessible
               | means. I'm talking accessible as in, 'I can literally
               | access this', not as in 'I can understand what this
               | means'.
               | 
               | I use a screen reader, and unless the pdf is explicitly
               | created as an accessible pdf, it is just garbled up
               | nonsense.
        
               | xyzzyz wrote:
               | Yes, they should, and rendered PDFs are accessible to
               | readers.
        
             | colechristensen wrote:
             | Someone, perhaps, but in general, not particularly. PDFs
             | are just fine for the machine readability that almost
             | everyone wants.
        
               | IshKebab wrote:
               | Not the kind of machine readability that he was talking
               | about and you know it.
        
               | simonh wrote:
               | But if practically nobody wants it, is that a real
               | problem?
        
           | trident5000 wrote:
           | Do both
        
         | mhh__ wrote:
         | Just do both.
         | 
         | It's a flaw with latex as far as I'm concerned.
        
       ___________________________________________________________________
       (page generated 2022-08-04 23:00 UTC)