  Finding affine parameters for null geodesics is often of considerable
physical importance, especially when studying the paths swept out by null
geodesics or when dealing with conservation laws and/or averaged energy
conditions. But explicitly finding null affine parameters is also often quite
tedious and can sometimes even be somewhat tricky. Herein we shall demonstrate
that the existence of a conformally related spacetime containing a conformal
Killing vector, timelike in the domain of outer communication, is quite
sufficient to define a preferred set of spatial three-slices -- on which a
well-defined "affine" three-metric can be introduced to capture the notion of
affine null parameter -- before explicitly finding the null geodesics. The
construction depends on the properties of conformal transformations and on the
conserved quantity associated with the conformal Killing vector. Having the
affine null parameter in hand before attempting to find the actual null
geodesics often quite radically simplifies other parts of the analysis. We
emphasize that the successful identification of affine null parameters is a
general-purpose tool of wide applicability in both general relativistic and
astrophysical settings.
