Mathematical prerequisites for general relativity

[accdd]

What mathematical topics do I need to know to start studying general relativity?
From which textbooks can I learn them?
I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and some special relativity.

 

[ergospherical]

Your pre-requisites are fine and intro gr texts will teach you about the mathematical machinery you need. Don't bother learning diff geom from a maths book at this stage (unless you want to, of course). If you can learn to push around tensor indices without thinking, you're halfway there.

 

[PeroK]

What mathematical topics do I need to know to start studying general relativity?
From which textbooks can I learn them?
I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and some special relativity.

I agree with @ergospherical, with your maths knowldege you should get started on GR directly. Sean Carroll's book is a good introduction that you should be able to work from. There are also these MIT lectures from a graduate course in GR that are very good. They start with a review of SR from the geometric viewpoint:

https://ocw.mit.edu/courses/8-962-g...ction-and-the-geometric-viewpoint-on-physics/

 

[Ibix]

If you can learn to push around tensor indices without thinking, you're halfway there.

The other half is learning to swallow vectors as differential operators.

 

[PeroK]

PS Sean Carroll's notes are available here:

https://www.preposterousuniverse.com/grnotes/

 

[Orodruin]

The other half is learning to swallow vectors as differential operators.

Only the tangent vectors. The cotangent vectors are linear maps from local first order linear differential operators to the real numbers.

Other than that, I can just repeat what has been said: You need multivariable calculus, linear algebra, some differential equation solving skills. Apart from that most introductory books will include what maths you need. Of course, nothing stops you from reading about differential geometry in some well chosen mathematical methods text. It is also quite applicable to other areas in physics.

 

[Jamestein Newton]

If you are talking Wald's level (the most hardcore one). You will need Riemannian geometry. People would also read Wald GR together with John M lee's intro smooth manifolds.

I don't think you need to concern too much if you were not using such a hardcore book. People just learn the maths when they read from their physics textbook