Conservative Moment Equations for Neutrino Radiation Transport with Limited Relativity

Understand

We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations.

• After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits.
• Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature.
• The third limit is a weak-field, `pseudo-Newtonian' approach \citep{kim_etal_2009,kim_etal_2012} in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity $v$ are retained.