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In the Catalogue of Spacetimes, in the Kerr metric section, under "General local tetrad", there is a cluster of four equations (strangely labeled 2.14.6a and 2.14.6b!), two of which contain the symbol $\zeta$. It also appears in 2.14.7. As far as I can see that symbol is not defined anywhere, although it looks like it is probably some sort of angular quantity, being mostly associated with $\phi$.

Can anyone here shed some more specific light on what that symbol represents?

[EDIT] If I were to guess, I would say it is a measure of "rotation" of the tetrad with respect to the "distant stars", so that a "non-rotating" tetrad would actually have to rotate "counter" to the black hole (in some sense) in order to remain pointing at a distant star ($\omega = - \zeta$). Similarly a "static" tetrad would still need to rotate (by doing nothing, $\zeta = 0$, ?) to maintain its orientation with respect to the black hole. All guess work though . . .

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$\zeta$ is just a parameter that you can choose for yourself. It's a "general tetrad" after all. It looks like an angular velocity, but in the next equations they spcify a "non-rotating" tetrad that still has an $\zeta=\omega$ angular velocity, but I assume that this is because the frame dragging makes the notion of "non-rotating" ambiguous: are you non-rotating with respect to the distant stars, or to the event horizon.

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