While reading this article I got stuck with Eq.[itex](54)[/itex]. I've been trying to derive it but I can't get their result. I believe my problem is in understanding their hints. They say that they get the result from the Gauss embedding equation and the Ricci identities for the 4-velocity, [itex]u^a[/itex]. Is the Gauss equation they refer the one in the wiki article?(adsbygoogle = window.adsbygoogle || []).push({});

Looking at the terms that appear in their equation it looks like the Raychaudhuri equation is to be used in the derivation in order to get the density and the cosmological constant, but even though I realize this I can't really get their result.

Can anyone point me in the right direction?

Thank you very much

[itex]Note:[/itex]The reason why I'm trying so hard to prove their result is because I wanted to know if it would still be valid if the orthogonal space were 2 dimensional (aside some constants). It appears to be the case but to be sure I needed to be able to prove it.

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# Ricci tensor of the orthogonal space

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