# Linearized Einstein Field equation in general background

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?

• It is done in Straumann's book Feb 19 '20 at 8:38
• You can find the answer to your question here - physics.stackexchange.com/a/487808/133418 Feb 21 '20 at 15:47
• @Avantgarde Thanks! After confirming the first order computation by hand I will use xPert for higher-order computation! Feb 23 '20 at 5:36