GR: How Much Mechanics is Involved?

[vector]

I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite comfortable in Applied Math, and, to a certain degree in Pure Math (especially Abstract Algebra). I've also taken Quantum Mechaics, and got a very good mark in it, one of the highest marks ever (compared to other courses).

My question is: how heavy is General Relativity on the side of Mechanics? I sincerely hope that it has "too much" "hardcore math" than it has any "hardcore mechanics".

 

[Simon Bridge]

GR is mechanics ... but how much the GR course leans on the Mechanics prereq really depends on the school.

 

[vector]

If that's the case, it seems that I'll have to take Differential Geometry instead. I was really looking forward to learning GR, including the Differential Geometry part of it, but I have a bit of a trouble with Classical Mechanics.

Actually, a course in Quantum Theory in my school also has Theoretical Mechanics as a prerequisite. Does this mean that QT courses also depend a lot on Classical Mechanics stuff? The introductory QM course I took contained almost no Classical Mechanics.

 

[sweet springs]

I think the combination of QM and GR should be explored to complete mechanics.

 

[vanhees71]

The most important prerequisites for GR are linear algebra and vector calculus as well as the calculus of variations (I believe that without the action principle you have no chance to understand anything in physics beyond "naive" Newtonian mechanics). A course in differential geometry is very helpful to learn GR, because the only difference between GR and differential geometry is that the latter is the theory of Riemannian manifolds, while GR is based on a pseudo-Riemannian manifold. The difference is physically very important but mathematically it's not a big step. More important than analytical mechanics (i.e., the mechanics of point particles based on the action principle) is a good foundation in classical field theory (a modern course on E&M, using the manifest covariant notation in special relativity and the action principle for fields is enough). There's no need for QM to learn GR, which is an entirely classical field theory.

 

[vector]

vanhees71, thank you for your detailed post. From your post, it appears that Classical Mechanics is not extensively applied in GR, and that GR is quite abstract. Which would be good for me, because I seem to lack some intuition for Classical Mechanics, and do prefer more abstract courses, like QM.

 

[pixel]

Why not browse through the GR textbook that the course is using, or speak with the prof? It seems introductory GR courses involve a lot of upfront math before even getting to any physics.