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  Ricci scalar in perturbation theory

+ 2 like - 0 dislike
104 views

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 in Theoretical Physics by fermionic_tushar (40 points) [ revision history ]
edited Jul 16 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 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.

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