Tensors, metrics, differential geometry, and all that

[disknoir]

I'm looking to learn general relativity, but I'm having a hard time. Frankly, I can't find any textbooks that I can understand.

There seems to be a gap between the maths I did at uni, and the maths of general relativity.

I've done vector calculus, differential equations, linear algebra and complex analysis etc, but I just can't seem to find any resources to bridge the gap.

While at uni, I mostly used the k.a. stroud engineering mathematics books.

Do I need to re-visit some of this from a more rigorous angle? I'm getting quite frustrated, as I no-longer have a tutor or class mates to discuss things with.

I'm starting a course in general relativity in February, and really want to get a head start.

I'd like to know what maths I need to learn to fill in the gaps in my knowledge, and in what order I should learn them.

Advice/book recommendations would be great.
Thanks

 

[yicong2011]

My favorite GR introductory books are Wolfgang Rindler's "Relativity: Special, General and Comological" and Ray de'Inverno's "Introducing Einstein's Relativity". Ray de'Inverno's book provides you lots of exercises on tensor calculus. Most of his exercises are straightforward, easy-to-do, but can help you to build up skills. Bernard Schutz's "A First Course in General Relativity" is also nice: many undergraduate GR books shun to discuss "differential forms" , but Bernard Schutz does not omit this.

 

[disknoir]

Thanks.

Luckily, I have access to an academic library; I'll have a look for them.

 

[Daverz]

For GR, Hartle takes a physics first approach that will get you into applications faster.

https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20

If you want a book that explains the mathematics thoroughly, you could try Dodson & Poston.

https://www.amazon.com/dp/354052018X/?tag=pfamazon01-20