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 . . .