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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 useseinstein's equationon the unperturbed metric to fish out [itex]\delta R_{ab}[/itex], then uses that to deriveeinstein's equationwith 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

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# Hilbert action according to robert wald

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