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I am trying to compute Linearzed Einstein Field equation in general background.

I mean $g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}$ and compute R, $R_{\mu\nu}$ and so on.

I realized the computation is quite handy, and I even don't know my computation is right or not.

Is there any reference for metric perturbation in general background?

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    $\begingroup$ It is done in Straumann's book $\endgroup$
    – Slereah
    Feb 19 '20 at 8:38
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    $\begingroup$ You can find the answer to your question here - physics.stackexchange.com/a/487808/133418 $\endgroup$
    – Avantgarde
    Feb 21 '20 at 15:47
  • $\begingroup$ @Avantgarde Thanks! After confirming the first order computation by hand I will use xPert for higher-order computation! $\endgroup$
    – phy_math
    Feb 23 '20 at 5:36
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As with many topics in general relativity, Wald gives a fairly good treatment of the general case in his book "General Relativity", in this case in section 7.5.

It is one of the few "standard texts" in GR I found that actually treats the general case. Many others (e.g. MTW) restrict to perturbations of flat space, or immediately specialize to black hole perturbation theory.

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