Is it true that in all spacetimes there is some conformal time-like Killing vector $\tau^a$ in the vicinity of null geodesics?
If the above statement is true then can one argue that, for all spacetimes, an EM wave propagating along a null geodesic with wave-vector $k^a$ has a conserved quantity $k_a\tau^a=k_\tau$?
Please see @MichaelSeifert's informative answer and comments for background to Killing vectors, conserved quantities and EM waves:
