# What are the quadratic order fluctuation terms for curvature tensors about some background metric?

+ 2 like - 0 dislike
345 views

Like one can see the linear order terms on page 18 here, http://www.ugr.es/~bjanssen/text/fierz-pauli.pdf

- I would like to know of a reference for the derivation of the quadratic order terms for the Riemann tensor, scalar curvature and Ricci tensor and for $\sqrt{-g}$?

- Further on such an expression how does one impose that the background is say $AdS$? (even for the linear case as linked above)

- Is there a way by which Mathematica can be made to derive these expressions?

edited Jun 8, 2014

+ 2 like - 0 dislike

- I would like to know of a reference for the derivation of the quadratic order terms for the Riemann tensor, scalar curvature and Ricci tensor and for $\sqrt{-g}$?

Many introductory GR books and lectures: Carroll, Weinberg, Feynman lectures on gravitation, Misner, etc. You should work it out on your own, though. You just need to split the metric in a background plus a fluctuation and treat the fluctuation as a tiny perturbation.

- Further on such an expression how does one impose that the background is say $AdS$? (even for the linear case as linked above)

The background metric is the AdS metric instead of Minkowski. What in a flat background are the components of Minkowski metric are the components of AdS.

answered Jun 10, 2014 by (885 points)

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:$\varnothing\hbar$ysicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.