General relativity

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1. omnicognateNov 2025
   That's good to know about Wald. I bought a copy to finally get my head round General Relativity, but its brief explanation of Special Relativity right at the start made it clear that I hadn't properly understood that, which led to me getting Gourgoulhon's book. I should be better placed to tackle it now.
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2. raattgiftMar 2024
   There is a relationship in that both the "Spongebob cluster" and a black hole has negative heat capacity. The math is already there in the virial theorem. See <https://en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...>. Detailed treatments of the non-relativistic case you can find in an undergrad astronomy textbook; the relativsitic singleton case ehhhhh I don't think you're ready for it but Wald's General Relativity §12.5 & §§14.3-14.4 would be a good choice (and he shows you the math, which has been known for several decades), and for relativistic orbits I think you need to go beyond textbooks (although you probably could start with numerical relativity textbooks, like Baumgarte & Shapiro or Alcubierre, although I don't have either handy to double-check where they go with thermodynamics. Oh and the paper I linked in a sibling comment has a good and relevant bibliography. <https://academic.oup.com/mnras/article/516/3/3266/6668807>).
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3. DiogenesKynikosNov 2022
   > When looking at spatial distances, we usually want to look at spatial coordinates.

   That's not the case, because most objects we're measuring distances to are not at the same coordinate time as us. In fact, these objects are generally in the past.

   If you're trying to measure the distance to an object that you've observed, that object is, in fact, along your past light cone. The only coordinate-invariant distance that one can actually define, the metric distance, is zero. That means you have to define an alternate type of distance. Some of those choices (like the comoving distance) don't depend on a(t), while some do (like the light travel distance).

   > All of this is explained pretty well on wikipedia, but if you want you can also take a look at Hartle's or Carroll's textbooks on General Relativity.

   I prefer Wald, which is much more mathematically rigorous than Carroll. I haven't read Hartle, so I can't comment on it.

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4. ummonkMar 2022
   The post was also a poor explanation for someone doing modern physics. [edit: not true actually I should have read the rest of the post - it’s a good post]

   Wald's approach in General Relativity is much better - he treats Tensors as a multilinear map from vectors and dual vectors to scalars.

   He then derives the underlying coordinate transformaton rules, for the vector spaces used in differential geometry. But

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5. ummonkMar 2022
   Not all physicists make that conflation - Wald’s book in General Relativity emphasizes tensors as abstract concepts, and then details how they can be expressed in terms of a basis.

   The OP also emphasizes the abstract interpretation as providing more intuition than the coordinate transformation rule.

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6. pa7x1Aug 2020
   There might be better or more modern references for Differential Geometry but I enjoyed Barrett O'Neills' book.

   https://www.elsevier.com/books/semi-riemannian-geometry-with...

   Also Misner-Thorne-Wheeler and Wald's book on General Relativity.

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