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Hilbert action according to robert wald

  1. Jun 22, 2012 #1
    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
    Last edited: Jun 22, 2012
  2. jcsd
  3. Jun 22, 2012 #2


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    Carroll's derivation seems pretty straight forward (see pg. 114): http://preposterousuniverse.com/grnotes/grnotes-four.pdf [Broken]
    Last edited by a moderator: May 6, 2017
  4. Jun 25, 2012 #3
    thanks very much, that is an easier method. good work.
  5. Jun 25, 2012 #4


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    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).
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