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. 
Christian Y. Cardall (1 and 2), Eric J. Lentz (1, 2, and 3), Anthony   Mezzacappa (3) ((1) Oak Ridge National Laboratory, (2...