What is the bare Minimum Lagrangian\Hamiltonian mechanics

[cpsinkule]

I am currently trying to self learn general relativity. I understand you need knowledge of an action principle, but what I am not so sure of is how deep of an understanding I need. I currently have a book on classical field theory and I am at the point of basic Lagrangian's and holonomic systems. I can compute lagrangians and I am very familiar with the E-L equation, but I have yet to come to non-linear dynamics and hamiltonian mechanics. My question boils down to how much do I need for an introduction to G-rel?

 

[Fredrik]

GR is the theory that says that spacetime is a smooth manifold with a metric that satisfies Einstein's equation. A derivation of Einstein's equation from an action principle wouldn't even be a part of the theory. That derivation is also not included in most introductory courses, because it requires an understanding of integration of manifolds. So I'd say you don't need any knowledge of Lagrangian mechanics at all.

 

[cpsinkule]

thanks so much, I was worried id have to drudge through the other 600 pages of this book, however I was under the impression that any physical theory usually has a side-kick action formulation (i have several books on grel, but wald's was the only one to mention it)

 

[PAllen]

Well, I have GR books ranging from 1921 (two of them) to 1973 (MTW). All describe derivation of the field equations from an action principle. I would agree that in most of this is dealt with as a side topic that could be dispensed with without major loss. However, even an old, first course like Bergmann's 1942 book gets the vacuum field equation without variation, but introduces matter and EM fields via Hamiltonian to get appropriate stress energy tensor.