  Models for the observational appearance of astrophysical black holes rely
critically on accurate general-relativistic ray tracing and radiation transport
to compute the intensity measured by a distant observer. In this paper, we
illustrate how the choice of coordinates and initial conditions affect this
process. In particular, we show that propagating rays from the camera to the
source leads to different solutions if the spatial part of the momentum of the
photon points towards the horizon or away from it. In doing this, we also show
that coordinates that are well suited for numerical General-Relativistic
MagnetoHydroDynamic (GRMHD) simulations are typically not optimal for generic
ray tracing. We discuss the implications for black-hole images and show that
radiation transport in optimal and non-optimal spacetime coordinates lead to
the same images up to numerical errors and algorithmic choices.
