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I've been studying General Relativity for a while from physics books and I could understand most of the materials. My problem is I'd like to study the mathematics of GR to really understand the subject as well as its formulation.

I have a background in physics, so I'm asking in here for a mathematician's point of view. And what I am looking for is a path and resources from calculus to all of the mathematics which has been used in GR. I say from calculus because as a physics major, they haven't taught us thoroughly and rigorously like how mathematicians study it so I'm willing to study from scratch.

And also I started a book on General Relativity for Mathematicians and I couldn't understand anything. So I was hoping I could start from somewhere which could lead me to that book on the end.

I'm sorry because this question is similar to others but I couldn't find any answer to my question.

Ben Grossmann
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Mohammad Nourbakhsh
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  • Check this question and the ones linked there https://math.stackexchange.com/q/3769113/532409 – Quillo Mar 14 '24 at 08:31

2 Answers2

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I think the missing piece between calculus and general relativity that you need is a general introduction to Riemannian geometry. Note that you want a general one and not one that restricts to surfaces (general here referes to the dimension of the manifolds under study). Do Carmo is a classic, but there are others.

If you understand Riemannian manifolds well, the mathematicians book on general relativity should be understandable. If you are missing some prerequisites for Riemannian geometry an introduction to real analysis should work (I used Rudin when I learned it but there are a lot).

quarague
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Check out A Mathematical Introduction to General Relativity .

It is targeted at mathematics undergraduate students and develops semi-Riemannian geometry from scratch (only prerequisites are multi-variable calculus and linear algebra). A preview of the contents and a sample chapter can be seen at the website above. As it contains solutions to all the exercises, it can be used for self-study.

Amol Sasane
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