My question is about defining positive frequency modes of radiation in a generic (static) spacetime. I mean, take a black hole and Eddington-Finkelstein null coordinates; $u$ and $v$ are Killing coordinates respectively on past and future horizons. Now I know that in a generic static spacetime I can define positive frequency modes through timelike killing vectors; I'm a bit confused because studying collapsing black holes, as far as the asymptotically flat regions are concerned, I can define positive frequency radiation modes as $e^{-i \omega v}$ (same with $u$). How can I do it if killing parameters $u$, $v$ are lightlike and not timelike?


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