Numerical treatment of the spherically symmetric general-relativistic Boltzmann equation for massless and massive particles

The Arnowitt-Deser-Misner formalism is used to write the Einstein-Boltzmann coupled system of equations. The sources of gravitational field are represented by ordinary matter described by a perfect-fluid approximation together with a particle gas described by a phase-space distribution function obeying the general-relativistic Boltzmann transport equation. Through the use of the Liouville operator in phase space, we obtain a form of the Boltzmann equation that makes it very amenable for numerical treatment. The resulting system of equations can be used for the numerical study of either massless or massive particles interacting with ordinary matter.