Radiative transfer along rays in curved space-times

Radiative transfer in curved space-times 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 non-geodesic) path, thus reducing the problem of radiative transfer along a ray to a path integral in coordinate space.