Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations

TL;DR

This paper develops conservative 3+1 general relativistic radiation transport equations using the variable Eddington tensor, suitable for complex astrophysical simulations involving neutrinos and dynamic spacetimes.

Contribution

It introduces a detailed formulation of the radiation transport equations with an emphasis on momentum space divergence and conservation properties in general relativistic contexts.

Findings

Equations are formulated for use in numerical relativity simulations.

Ensures consistency of four-momentum and lepton number exchange.

Provides detailed treatment of energy derivative terms in the transport equations.

Abstract

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. 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 pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.