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~0.1c can occur in these systems, it has been common practice to approximate radiative transfer to O(v/c). In the case of neutrino transport in core-collapse supernovas, this approximation gives rise to an inconsistency between lepton number transfer and lab-frame energy transfer, which have different O(v/c) limits. A solution used in spherically symmetric O(v/c) simulations has been to retain, for energy accounting purposes, the O(v²/c²) terms in the lab-frame energy transfer equation that arise from the O(v/c) neutrino number transport equation. Avoiding the proliferation of such extra O(v²/c²) 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.