  It has now become possible to study directly, via numerical simulation, the
evolution of relativistic, radiation-dominated flows around compact objects.
With this in mind we set out explicitly covariant forms of the radiative
transfer equation that are suitable for numerical integration in curved
spacetime or flat spacetime in curvilinear coordinates. Our work builds on and
summarizes in consistent form earlier work by Lindquist, Thorne, Morita and
Kaneko, and others. We give explicitly the basic equations in spherical-polar
coordinates for Minkowski space and the Kerr spacetime in Kerr-Schild
coordinates.
