Spacetime and geometry
by Sean M. Carroll · first published 2003
89% recommend11% neutral
Why HN recommends it
Clear, well-motivated graduate textbook on general relativity that explains definitions and builds the math with exercises; makes GR accessible to mathematically minded students and working learners.
Summarised by Claude from recommending comments
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…Although intended to be self contained in principle, it also might serve as a good jumping off point to further study in a particular area. For general relativity, I really recommend Sean Carroll's book Spacetime and Geometry http://preposterousuniverse.com/spacetimeandgeometry/. If it seems like a long road ahead just take it one step at a time. You'll get there.
on “Theoretical Physics, In Your Own Time” ↗I'm not sure what I would recommend as an introduction to relativity. If you're mathematically minded and have a lot of time on your hands, and actually want to learn the physics, a superb book is "Spacetime and Geometry" by Sean Carrol. As for a layman introduction, I'm not sure what to recommend. As succinctly as I can put it, in our current understanding spacetime is a 4-dimensional space whose curvature is related…
on “Carlo Rovelli on the ‘greatest remaining mystery’: The nature of time” ↗…bodies differently. An inertial observer in this asymptotically flat spacetime at a great distance and not feeling the GWs will see the system precess.[3] Chapter 7 (Perturbation theory) in Carroll's _Spacetime and Geometry_ in subchapters 7.4-7.6 has a reasonably good inductive view of the mathematics in the limit of weak gravity, and the time-reversal trick should be workable with the contents of the chapter. You could…
on “Gravitational waves eject black hole from galaxy” ↗You could also check out Sean Carroll's Spacetime and Geometry. It's my favorite textbook. Supplement with the second half of Wald's book for exploring some concepts
on “Spacetime Calculus [pdf]” ↗For a textbook where the author does a brilliant job of introducing a complex topic: Spacetime and Geometry an Introduction to General Relativity by Sean Carroll. Also the textbooks by David Griffiths and Gill Strang mentioned in other comments.
on “Ask HN: What's the best textbook you've read?” ↗I'm working through Sean Carroll's "Spacetime and Geometry". So far it's been quite accessible and is replete with exercises. Carroll's explanations do a really good job of motivating definitions while also introducing deeper, beautiful math. It's not all just…
on “Eldar Black Holes” ↗For general relativity: I never miss an opportunity to recommend "Spacetime and Geometry" by Sean Carrol. The only book I needed for my GR course (plus Misner Thorne and Wheeler for occasional reference).
on “Stuff I Learnt in 2019” ↗Sean Carroll is incredible, and his textbook on Spacetime & Geometry was the only reason I understood anything in my graduate-level class on general relativity. There's truly an art to be able to explain incredibly complex topics in an easy(er) to understand way.
on “Wormhole Tunnels in Spacetime May Be Possible, New Research Suggests” ↗Google won't help you here. Popsci stuff is useless at best, and more often actively misleading. You need a GR textbook. An Introduction to General Relativity, Spacetime, and Geometry (https://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Carroll_S...) is relatively accessible.
on “What Is Our Universe Expanding Into?” ↗…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 off with e.g. Carroll's Spacetime and Geometry or Wheeler's Gravity and Spacetime. There is also the Israel-Darmois thin shell method, which is technically annoying but lets us cut the central part of an e.g. Schwarzschild solution and paste it into…
on “Research suggests Big Bang may have taken place inside a black hole” ↗…should not diminish the original works. There are probably much better communicators/teachers of relativity than Einstein ever was. No one out there thinks any less of Einstein because of Sean Carrol's "Spacetime and Geometry" textbook. And this to me reads as only embracing the use of AI in mathematics, which is not gatekeeping behavior. Tao continues to emphasize that once proofs become effectively automatable, deeply comprehending…
on “Terence Tao: Math 2.0 [pdf]” ↗…materials. I don't remember whether the book introduces bra-kets (Dirac notation) or assumes them, and I don't remember if Griffiths uses it at all. I first saw this notation in General Relativity, with Spacetime and Geometry [3], but I think there are definitely better materials that can explain the notation better. I'm pretty sure all of these books, and plenty more on these topics, should be widely (or freely) available.…
on “What is quantum field theory and why is it incomplete?” ↗