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Ok, in your work you used Ricci calculus with Latin indices (although Latin indices are typically used in abstract index notation).PeterDonis said:Putting the above together, we see that the ##\gamma \omega / R## terms cancel and we are left with
$$
\mathscr{L}_U E = - \gamma^3 \omega^2 R \left( \partial_T + \omega \partial_\Phi \right)
$$ which equates to ##A \hat{p}_0##.
From Insights article ##\Omega = \gamma^2 \omega## and ##\hat{p}_3 = \gamma \omega R \partial_T + \frac{\gamma}{R} \partial_{\Phi}##, so the above calculation of ##\nabla_{\hat{p}_2} \hat{p}_0## is not equal to ##\Omega \hat{p}_3##.PeterDonis said:Note that this is actually not the same result I had given in an earlier post; we can also see that ##\nabla_{\hat{p}_2} \hat{p}_0 = \Omega \hat{p}_3##, which makes more sense than what I had incorrectly computed in that earlier post.)
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