7 ms·

>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

• V__ 4y ago
  > 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.
• Victerius 4y ago
  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%
  • dylan604 4y ago
    The assignment website to upload work keeps telling me that my upload is too big. It says there's a 900 page limit
    • lapetitejort 4y ago
      "Just... cut a few." "Which pages do you have in mind, professor?"
      • dylan604 4y ago
        the one with the final answer of course. you get majority of credit from showing your work
  • sidlls 4y ago
    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.
• rrishi 4y ago
  At 912 pages, thats a book not a paper (i jest)
  • sharkweek 4y ago
    > (i jest) Infinite Jest? 70 pages longer (if you don't include the footnotes)
    • rrishi 4y ago
      i meant that i was kidding calling it a book.
      • baq 4y ago
        at 2100 pages it's a trilogy, so yeah...
  • samstave 4y ago
    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 4y ago
    Oh come on. You'd often get that much for an MCU part and they call it a (data)sheet.
• curt15 4y ago
  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/the-global-nonlinear-stability-of-the-minkowski-space-pms-41 https://press.princeton.edu/books/hardcover/9780691632551/th...
• codethief 4y ago
  > 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 4y ago
    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-undergraduates/what-you-can-learn-applied-mathematics/relativity-and-cosmology https://uwaterloo.ca/applied-mathematics/future-undergraduat...
    • layer8 4y ago
      A forming the basis of B doesn’t imply that everyone working on A will be considered a B-ologist.
      • ziddoap 4y ago
        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.
    • codethief 4y ago
      As the sibling said, even if you consider cosmology a subfield of GR (which it is only to a small degree), not all relativists will be cosmologists. But you wanted me to expand on this a bit, so here you go: Cosmology is concerned with the cosmos as whole, i.e. the largest scales of the universe. GR looks at large scales, but not necessarily the largest ones. (A typical black hole is much smaller than a galaxy.) But this is not the only difference between the fields: General Relativity is just one tool inside a cosmologist's toolbox. Most of them also need quantum field theory, statistics and image processing in their daily work. The reason is that, while Relativity by itself is usually only concerned with theory, and mathematical GR even more so, cosmologists have to match their theories to actual observations. They are interested in the history of the universe and in the large-scale (average) behavior of what you can see on the sky. Meanwhile, mathematical GR is mostly a mathematical endeavor. People in that field tend to be mathematicians, with a background either in analysis / PDE theory or in geometry or both (geometric analysis). They are interested in physics-inspired questions but not exclusively so.
• WebbWeaver 4y ago
  I'm definitely going to go in there and find out how they defined 'slowly rotating.' I bet its pretty cool.
  • walnutclosefarm 4y ago
    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.
  • raattgift 4y ago
    tl;dr: gravitational waves do hard-to-calculate things inside a strong ergoregion around a fast-spinning black hole, and may do hard-to-calculate things to the black hole, and those calculations are outside the scope of the paper. > [how to define] 'slowly rotating' [might be] pretty cool It's for a pretty cool reason. Bear in mind that I am not a superhuman so have not read the 900-page document rather than scanning through the most interesting bits. Also, forgive me, I got a bit lazy and have left in a bunch of redundancy below rather than trimming it out or reorganizing it. The question in a nutshell is to whether any setup of initial conditions that are reasonably similar to a Kerr spacetime will settle into another set of conditions reasonably similar to Kerr spacetime eventually. The conditions are roughly (eternal!) Kerr black hole in the distant distant past plus a bunch of gravitational radiation to it's "left" travelling rightwards. The "present" is the collision of the waves and the black hole. The far far future is the remnants of the gravitational waves waaay to the black hole's right, plus the original black hole (albeit with a slightly different spin or mass). There is never anything but gravitational waves and the black hole. How do we know from the mathematics of General Relativity that the far-future black hole still spins at all? Or that it hasn't self-destructed? Does this hold up even as we add more gravitational waves coming from different directions? That's what the authors set out to show. Lumpy, slowly rotating noncompact (i.e. entirely outside of their Kerr horizons) self-gravitating objects see their surfaces smooth out over time through various processes. Stars find themselves in hydrostatic equilibrium even as things fall into them. Planets are defined as being in hydrostatic equilibrium: their lumpiness and tumbling fades away and tends towards being nearly spherical and spinning around a single axis, even though rocks or ice might fall onto them from time to time. <https://en.wikipedia.org/wiki/Hydrostatic_equilibrium#Astrophysics https://en.wikipedia.org/wiki/Hydrostatic_equilibrium#Astrop...> <https://en.wikipedia.org/wiki/List_of_gravitationally_rounded_objects_of_the_Solar_System https://en.wikipedia.org/wiki/List_of_gravitationally_rounde...> A "peaceful" black hole horizon is highly analogous to the surface of a body in hydrostatic equilibrium. There are some differences here: we can throw "too much" at a rocky planet or star, totally disrupting them. You can't break apart a black hole in the setting under consideration (and likely not at all). You can "bounce" a rock with a glancing blow off a rocky planet, maybe turning the planet into something like Earth-Moon. Again, you can't split a black hole, and you can't bounce something off a black hole's event horizon. You can throw too much at a star and create a supernova. You can't explode a black hole that way. So we want to restrict our analogizing to the case where a relatively small body lands on (but does not destroy or blow chunks out of) a rocky body or star. Also, while we can spin a star or planet so fast that it disintegrates, we can't do that to a black hole. A glancing blow interaction might speed up the spin of a star or planet, possibly making it spin so fast it rips apart. Spinning a black hole as fast as you can does weird things in the immediate neighbourhood of a black hole, but should not rip the black hole apart. The paper sets out to prove that. The Kerr stability conjecture that is central to this paper considers the case where the Kerr black hole is perturbed by gravitational radiation "thrown" at it. The black hole relaxes back into Kerr (this is "stability for Cauchy data"). The paper also considers the case where if you are sufficiently far from the perturbed black hole you only see Kerr anyway when light-speed news of the event catches up to your gravitational-wave observatory (this is "stability for scattering data")). More colloquially, if you start with a slowly-spinning black hole and a (relatively distant) "mess" of gravitational waves, do you eventually end up with a slowly-spinning black hole (or something very close to it) or do you destroy your black hole? Going from "of course the remains of this sort of interaction must include a spinning black hole, because linearizations of General Relativity show that to be the case for black hole mergers" ("smash two black holes together, you get one bigger black hole and a bunch of gravitational radiation and we can see all of this at LIGO/VIRGO and other telescopes") to "here's a rigorous mathematical description in the full non-linearized theory of General Relativity that is good up to arbitrarily large incoming gravitational radiation: you always get a bigger (slowly spinning) black hole" is roughly the subject of the long paper discussed at the Quanta link and found at <https://arxiv.org/abs/2205.14808 https://arxiv.org/abs/2205.14808>. The size of a Kerr ergosphere -- the region outside the outer event horizon where things cannot remain still relative to the distant universe -- is determined by a combination of the black hole's mass and its spin angular momentum. If the mass/spin ratio is very high, then mass effectively determines the ergoregion's volume. A low spin also means the variation from the pole (where the ergo-effects are zero) to the equator (where they are strongest) is small. With a low mass/spin ratio (fast spin), the larger ergoregion can "hold" more gravitational radiation, and the strong ergo-effect leads to a stronger interaction between the Kerr black hole and any gravitational wave inside its ergoregion. This is even harder to calculate than the hardest equations in the paper. It is conceivable that the "held" gravitational radiation could be concentrated while within the ergoregion, and that if the ergoregion were large and strong enough, and the incoming gravitational radiation were "just so", a second black hole could form in the ergoregion from the collapse of the concentrated gravitational waves. In which case [a] would it be flung away to the far reaches of the universe [b] crash into the Kerr black hole merger-style or [c] hang around in a stable orbit near the black hole? [a] and [b], no problem, we have an "asymptotic" Kerr spacetime. [c]: big problem, because the spacetime is now like a barbell, and that sheds gravitational waves. (A single rotating black hole does not shed gravitational waves). These authors don't seem to say this outright, but they do cite an abundance of papers where the reasons proofs are harder as mass/spin approaches 1:1 are set out by their respective authors.