  Radiative transfer in curved spacetimes has become increasingly important to
understanding high-energy astrophysical phenomena and testing general
relativity in the strong field limit. The equations of radiative transfer are
physically equivalent to the Boltzmann equation, where the latter has the
virtue of being covariant. We show that by a judicious choice of the basis of
the phase space, it is generally possible to make the momentum derivatives in
the Boltzmann equation vanish along an arbitrary (including nongeodesic) path,
thus reducing the problem of radiative transfer along a ray to a path integral
in coordinate space.
