• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,741 comments
1,470 users with positive rep
818 active unimported users
More ...

  Ricci scalar in perturbation theory

+ 2 like - 0 dislike

This is a question regarding a calculation in perturbative GR. We have :

$g_{\mu\nu} = \eta_{\mu\nu}+h_{\mu\nu}$

where $h_{\mu\nu}$ is a small perturbation around the flat spacetime metric. In linearized theory, we ignore terms which grow as $h^2$ and higher.

Can anyone please provide me with the Ricci scalar to cubic powers in h?

asked Jul 16, 2019 in Theoretical Physics by fermionic_tushar (40 points) [ revision history ]
edited Jul 16, 2019 by Arnold Neumaier

No, none can provide you with the Ricci scalar to cubic powers in h. You will see that I am right, unfortunately.

1 Answer

+ 1 like - 0 dislike

Computation by hand will prove to be a bit tedious, but xACT software can do this in a matter of seconds. Here, is the expansion of the Ricci scalar to cubic orders around a generic background :

answered Jul 18, 2019 by fermionic_tushar (40 points) [ no revision ]

I suppose that $R=R(\epsilon=0)$, as well as $\eta_{\mu\nu}$, still are functions of "exact coordinates" $x_{\mu}$.

@fermionic_tushar Sorry can you tell me what xACT software is, provide a link or something? I'm curious but I didn't find much online.

Your answer

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):
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:
Then 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).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights