Conservative 3+1 General Relativistic Boltzmann Equation

Understand

We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric.

• The resulting transport equation is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry.
• The independent variables are lab frame coordinate basis spacetime position components and comoving frame curvilinear momentum space coordinates.
• With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we examine the relationship between lepton number and four-momentum exchange between neutrinos and the fluid.