Steps for solving the radiative transfer equation for arbitrary flows in stationary space–times

We derive the radiative transfer equation for arbitrary stationary relativistic flows in stationary space–times, i.e. for steady-state transfer problems. We show how the standard characteristics method of solution developed by Mihalas and used throughout the radiative transfer community can be adapted to multidimensional applications with isotropic sources. Because the characteristics always coincide with geodesics and can always be specified by constants, direct integration of the characteristics derived from the transfer equation as commonly done in 1D applications is not required. The characteristics are known for a specified metric from the geodesics. We give details in both flat and static spherically symmetric space–times. This work has direct application in 3D simulations of supernovae, gamma-ray bursts, and active galactic nuclei, as well as in modelling neutron star atmospheres.