General relativity
by Robert M. Wald · first published 1984
14mentions
8recommended by
10HN commenters
2011–2025first – last mentioned
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Why HN recommends it
A rigorous, mathematically careful graduate-level treatment of general relativity that shows the math in full, a standard reference for working physicists and advanced students who want depth over intuition.
Summarised by Claude from recommending comments
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…<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…
on “Gravitational Collapse of Spongebob” ↗As mentioned in a footnote in the blog post, I think Gelfand and Fomin’s “Calculus of Variations” is very clear on its topic. Wald's "General Relativity" is slow-going, but excellent. No good textbooks on quantum mechanics or QFT exist; Weinberg's "Quantum Theory of Fields" is probably the least terrible on that. Nielsen and Chuang's "Quantum Computation…
on “Structure and Interpretation of Classical Mechanics (2015)” ↗Reddit's r/AskScience recommended MTW's Gravitation[1], Wald's General Relativity[2], and, to begin, Sean Carroll's GR lecture notes[3]. Shameless affiliate links: [1] http://www.amazon.com/gp/product/0716703440/ref=as_li_qf_sp_... [2] http://rcm.amazon.com/e/cm?t=sdbo07-20&o=1&p=8&l...…
on “Einstein for Everyone ” ↗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…
on “Why tensors? A beginner's perspective” ↗The classic text is "Grativation" by Misner, Thorne, and Wheeler. It's very dense, but very thorough. The other classic is "General Relativity" by Wald. They don't really include the math background though, for that you need texts on multivariable calculus.
on “Rumours swell over new kind of gravitational-wave sighting” ↗…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.
on “Humanly Traversable Wormholes” ↗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…
on “Why tensors? A beginner's perspective” ↗…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.
on “Map of the observable universe” ↗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…
on “What is a manifold?” ↗…Understanding Power Textbooks: - order of 10^3 pages of Open University textbooks - Klauber, Student Friendly Quantum Field Theory - Feynman & Hibbs, Quantum Mechanics and Path Integrals - Wald, General Relativity (5 chapters) - Peskin & Schroeder, An Introduction to Quantum Field Theory (5 chapters) Not as bad as I felt before making the list, but underwhelming in terms of quantity. I intend to read a whole…
on “Ask HN: Books you read in 2015?” ↗I used these notes when I prepared the general relativity exam in my university years. I found them much clearer than Wald's "General Relativity", the textbook used in the class. However, when I had to prepare lecture notes for my own class on cosmology several…
on “Lecture Notes on General Relativity (1997)” ↗…textbooks on gravitational phenomena and theory, even reference papers which are now more than a hundred years old, oh no! Choosing a recent GR textbook -- Carroll 2014 -- the author lists under Advanced General Relativity: Hawking & Ellis 1973, de Felice & Clarke 1990, Sachs & Wu 1977; and in the Graduate section: Wald 1984, MTW 1973, Weinberg 1972, ...) > modern (2024-era) numerical methods which are built to be compatible…
on “Black Hole Puzzle” ↗…was mined in Sudbury, Canada). The curve of every part of a rock chucked through a black hole horizon ends inside the horizon. That curve-confinement is the characteristic feature of a black hole in General Relativity: no trapping surface, no black hole (Wald again, proposition 12.2.3). Where there is a trapping surface,no known high-energy behaviour of matter avoids collapsing gravitationally into a configuration…
on “Singularities in Space-Time Prove Hard to Kill” ↗…informal short-term tutor to walk you through particular things (you can find either at your local tertiary education school, like a community college or university), there are plenty of good textbooks on General Relativity. You seem to have found Wald's, which is probably the most rigorously and densely mathematical of several popular teaching choices, and it does not seem to have helped you. I'd guess you'd be better…
on “Research suggests Big Bang may have taken place inside a black hole” ↗