Conservative special relativistic radiative transfer for multidimensional astrophysical simulations: motivation and elaboration

Many astrophysical phenomena exhibit relativistic radiative flows. While velocities in excess of $v \sim 0.1c$ can occur in these systems, it has been common practice to approximate radiative transfer to \cO(v/c). In the case of neutrino transport in core-collapse supernovae, this approximation gives rise to an inconsistency between the lepton number transfer and lab frame energy transfer, which have different \cO(v/c) limits. A solution used in spherically symmetric \cO(v/c) simulations has been to retain, for energy accounting purposes, the \cO(v^2/c^2) terms in the lab frame energy transfer equation that arise from the \cO(v/c) neutrino number transport equation. Avoiding the proliferation of such ``extra'' \cO(v^2/c^2) terms in the absence of spherical symmetry motivates a special relativistic formalism, which we exhibit in coordinates sufficiently general to encompass Cartesian, spherical, and cylindrical coordinate systems.Comment: 9 page