Conservative 3+1 General Relativistic Boltzmann Equation

TL;DR

This paper derives a conservative form of the general relativistic Boltzmann equation in 3+1 form, facilitating numerical simulations of astrophysical phenomena like supernovae and mergers involving neutrinos and nuclear matter.

Contribution

It introduces a new derivation of the conservative relativistic Boltzmann equation tailored for 3+1 numerical relativity applications, especially for complex astrophysical scenarios.

Findings

Provides a form suitable for numerical relativity simulations

Clarifies neutrino-matter interaction in relativistic contexts

Lays groundwork for improved astrophysical modeling

Abstract

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.