In the Kerr spacetime, is it possible to find a null geodesic congruence which is non-twisting? I know that geodesics generated by the principal null directions are twisting. I know that there are spacelike non-twisting geodesics. But is there any null and non-twisting congruence of geodesics?
My first hunch says no. I haven't worked on this personally, but a non-twisting, null, geodesic congruence implies a fairly special spacetime. Then you only allow for the congruence to be expanding and shearing and this seems unlikely in a rotating spacetime like Kerr. Indeed, since the principal null directions are twisting is a signal that this is not possible. In Scharzschild spacetime the situation is different, so the rotation makes the difference here.
Hello, thank you very much for the answer. I had the same feeling (and many my colleagues), but there was some evidence that it is not correct; that's the reason of my question. Surprisingly, the answer turned out to be positive: you can construct non-twisting null congruence. If you start on the horizon (say, outer) and construct the Bondi-like coordinates, you automatically get non-twisting congruence emerging from the horizon and extending to the neighbourhood, and it apparently always exists. Very counter-intuitive result for me. Anyway, thank you for your answer.
Yes, this was interesting. So a follow-up would be: how local is this result? To what extent can you extend these geodesics?
The author claims it extends to scri (null infinity), so basically it is defined everywhere. I am talking about the paper by Badri Krishnan
http://arxiv.org/abs/1204.4345
But there is another paper
http://iopscience.iop.org/0264-9381/20/19/302/
where they construct Bondi coordinates in Kerr explicitly. But I didn't check yet whether it is the same as Krishnan does (in NP formalism).
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