8
$\begingroup$

I'm reading Zee's Einstein Gravity in a Nutshell and while calculating the Ricci tensor for FRW spacetime he claims that because the spacelike slices of constant $t$ are rotationally invariant, the off-diagonal elements of the Ricci tensor vanish (working in $t$, $r$, $\theta$, $\phi$ coordinates). Without calculating the Ricci tensor from the Christoffel symbols element-by-element, can someone provide an explanation of why this is true? More generally is there a good way to see how symmetries of the metric, like rotation or time translation, etc. translate to properties of the Ricci or Einstein tensor?

Improve this question
$\endgroup$
0

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.