Hilbert action according to robert wald

[naughtyeskimo]

hi everyone
i'm brand new to forums and I'm holdin a seminar on a variation of the hilbert action as described in wald's book general relativity. if anyone knows that book and topic pretty well maybe you can help me, my question is this:

for the variation [itex]\delta R_{ab}[/itex] with respect to parameter [itex]\lambda[/itex] of the ricci tensor [itex]R_{ab} [/itex] wald uses a result from the end of chapter 7, where he assumes [itex] g_0^{ab}[/itex] to be a solution of einstein's equation, so in the calculation of [itex]\delta R_{ab}[/itex] he assumes already that [itex]R_{ab} = 0[/itex] at $\lambda = 0$ so he works it out in terms of the tensor [itex]C^c_{ab}[/itex] (the tensor difference between two covariant derivatives).

my problem is: he uses einstein's equation on the unperturbed metric to fish out [itex]\delta R_{ab}[/itex], then uses that to derive einstein's equation with the hilbert action.

is there a good explanation for using this equation to derive this very same equation? i hope i explained myself clearly enough.

thanks in advance

 

[nicksauce]

Carroll's derivation seems pretty straight forward (see pg. 114): http://preposterousuniverse.com/grnotes/grnotes-four.pdf

 

[naughtyeskimo]

thanks very much, that is an easier method. good work.

 

[haushofer]

That's one reason I've never really liked Wald's book. Some things are being made much more complicated than necessary, unless you're a die-hard mathematician. Indeed, the easiest way is to apply the variation directly to the definition of the Ricci tensor and use covariance arguments (or do the whole calculation).