The large scale structure of space-time

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1. meiji163Sep 2022
   Some favorite math books

   Intro to Smooth Manifolds, Lee -- sweeping intro to geometry with minimal prereqs, great at balancing the nitty gritty details with conveying intuition

   A Course In Arithmetic, Serre -- classically terse and elegant intro to algebraic and analytic number theory. Goes from quadratic forms to Dirichlet's theorem to modular forms in a mere 100 pgs!

   Princeton Lectures in Analysis, Stein & Shakarchi -- 4 books covering much of classical/modern analysis, they really shine in their discussion of applications

   The large scale structure of space-time, Hawking & Ellis -- The most mathematically satisfying treatment of general relativity I've found. High points include proof of singularity theorems!

   Spin Geometry, Lawson & Michelson -- Deep dive into the enigmatic "spin groups" and their applications in geometry. Also the only good (book) reference I could find on the index theorem

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2. thisrodOct 2020
   > an adult can understand, but one that's been out of math for a while?

   That might not be possible. I remember struggling with the proofs of the singularity theorems, in the last year of my physics degree, after two semesters of differential geometry. Some of the things that people win the Nobel Prize for are genuinely hard.

   The Large Scale Structure of Space-Time is the classic. However, it's the book that Hawking was referring to in his joke about every equation halving the sales.

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3. dsqrtApr 2020
   I would also recommend "The Large Scale Structure of Space-Time" by Hawking and Ellis. It uses some advanced mathematics and some prior knowledge of GR, at least at the level of Schutz or Carroll, is needed, but it is a wonderful book to learn about the global structure of spacetimes with black holes, singularity theorems and so on.
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4. dalyDec 2024
   I'm reading "The Large Scale Structure Of Space-Time" by Hawking and Ellis

   One question is whether there is a singularity at the "bottom" of a black hole.

   It seems to me that the gravitational collapse at the singularity of a black hole would match the "trigger event" of the creation of our Universe.

   Within the (our) black hole there would be a singularity event which appears to us as the "creation of our Universe". Within such a black hole several effects likely occur.

   One is the "hologram" idea (https://www.scientificamerican.com/article/is-our-universe-a-hologram-physicists-debate-famous-idea-on-its-25th-anniversary1/) which posits that our universe’s 4D space­­time could be a holographic projection of a lower-dimensional reality. This would fit nicely if the "surface" of the hologram was the "surface" of the inside of our black hole.

   Another question arises as to whether the Universe is "infinite" and "what is it expanding into". Time and space would be extended toward the boundary of our black hole and would appear "infinite" but give something to "expand into" as both space and time would be changed when approaching the interior boundary of the hole. The boundary would appear to be "infinitely far away".

   There could likely be other "universes" within other black holes both within our current black hole and/or within black holes "outside of our universe".

   The "curvature of space-time" and the phenomena of "gravity" can be due to the "shape of the hole" from the inside.

   The "cosmic background radiation" could be due to Hawking radiation at the boundary where we see the particles that did not escape yet never able to see the corresponding particle that "boils off outside" our black hole.

   I refer to the idea of the Universe existing in "our black hole" as the Calcutta theory.

   Tim Daly

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5. cgeMar 2022
   Hawking was perhaps unusual in being both a very accomplished physicist and a very accomplished physics communicator, explaining the concepts of modern physics to the public. Sagan, I think, was neither a particularly accomplished scientist, nor seriously claimed or tried to be, unlike some modern science communicators, but was enormously accomplished in bringing science to the public. Many accomplished scientists would likewise be terrible communicating ideas to the public, and make little attempt to. Hawking was not Einstein, or Newton, but to argue that he did not make major contributions to research does not seem reasonable; nor is it reasonable to dismiss someone's contributions by comparing them to the most prominent contributors over multiple centuries.

   But Hawking did perhaps shift focus gradually from one to the other. It is hard to do research while also devoting so much time and effort explaining science to the public, and it is perhaps hard to maintain a serious scholarly perspective while focusing on simplifying concepts and explanations for a general audience. The fame itself can be an impediment, too. I can recall one scientist, somewhat famous for what was then somewhat of a side project, who noted with some annoyance that whenever he posted something on arXiv, it would be leapt upon by journalists who would contact him and the university asking about the paper's connection to the topic, when, of course, it had nothing to do with that. The authors of the Wikipedia article on The large-scale structure of space-time, meanwhile, find it necessary to repeatedly note that is not for a general audience, something not done for something like the phone book / MTW. The reviewer disagrees with the author on when Hawking stopped making significant contributions to science, but I think it can be generally agreed that he did, at some point, while still making major contributions to the popularity and public understanding of physics.

   I can remember one of my earlier experiences as a graduate student was going to what may have been one of Hawking's last research talks, in the mid-2000s. The group had to leave that week's meeting off the public departmental calendar that usually listed our seminar, lest the public swarm our small seminar room. He gave what remains, to this day, one of the most awkward and embarrassingly bad research talks I have ever been to. It entirely lacked rigour and seemed to make little sense at all. It almost felt like a talk an amateur fan of his would give about ideas they devised after reading his popular books. The sole question, from a prominent physicist whose name would likely be recognized here, but not to the public, was brutal, somewhat off-handedly dismissing the entire premise of the talk from basic physics considerations. Hawking's only response was to say that the questioner's argument might be right.

   Sadly, as the reviewer suggests, it may be that Hawking needed to shift his focus to popularizing science and courting the media in order to afford the care that would allow him to continue to live decently. It may not have been what he would have preferred. There are prominent scholars who continue to make significant contributions to research despite their age, who continue to be part of the scholarly conversation. The saddest part of the talk, when I thought about it later, was the sense that he seemed to almost be pleading with the audience to still be a participant in that conversation. He was an old friend of some of the faculty in the room. He had likely been one of the inspirations to more students in the room than just me, having read his popular works as a child and The Large Scale Structure of Space-Time a bit later. But I think it was clear to everyone that he was no longer part of the conversation. In science, at least, the name died before the man. Better it died, I think, by him moving into popularizing science than him moving into dubious quantum claims.

   After that seminar, he gave his public talks on campus, attended by enormous crowds; while he often returned to our campus, I don't recall him giving research talks again.

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6. boredguy8May 2010
   I'm really curious about how CBR observations solved the question related to universe size.

   Also, then, for me this makes me wonder: is then the big bang simply the origin of the null cone over whose event horizon we can't see? Clearly this is a Minkowski spacetime paradigm, and I have no idea where that stands in terms of general favor.

   Also: further reading? I'm guessing "The large scale structure of space-time" is a bit dated ;)

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