Math Courses Relevant to General Relativity

[diligence]

I'm a rising math major with a developing interest in General Relativity. I think the idea of studying Relativity from a mathematicians perspective sounds very appealing for graduate work. Besides differential geometry and partial differential equations, what are the most relevant pure math courses to this area of research? Also, how about applied courses as well as non-linear dynamics type stuff? Do this subjects find relevance in GR?

One of the reasons I ask is because I'm trying to decide if I should continue on to graduate-level algebra courses, as well as topology, or if I should just stick with analysis and geometry.



Thanks for any advice you may give.

 

[Sam Gralla]

I think mathematical relativists mainly use analysis, PDE, and of course geometry. It's not my field, however, so I wouldn't be able to give you totally sound advice. What I can do is list off some leading mathematical relativists, and you can look up their papers on arxiv.org to see what sort of techniques are being used. I'd look up Dafermos, Rodnianski, Christodoulou, and Kleinerman to start. The only one I know is Dafermos but he is very nice, and if you emailed him about it he would probably respond.

 

[robphy]

Group theory.
Calculus of Variations.

Numerical methods.
Fluid Dynamics. Classical Mechanics.

 

[cuallito]

Tensors.

 

[ballzac]

Tensors.

+1

Not all differential geometry courses use tensor notation, so I'd suggest doing one that does. I'm surprised no one has said linear algebra. I'm certainly no expert on GR, but I have studied it and from memory a basic understanding of linear algebra help with some of the manipulation of, for example, metric tensors, when actually looking for quantitative answers to a problem.