Implementation of a simplified approach to radiative transfer in general relativity

We describe in detail the implementation of a simplified approach to radiative transfer in general relativity by means of the well-known neutrino leakage scheme (NLS). In particular, we carry out an extensive investigation of the properties and limitations of the NLS for isolated relativistic stars to a level of detail that has not been discussed before in a general-relativistic context. Although the numerous tests considered here are rather idealized, they provide a well-controlled environment in which to understand the relationship between the matter dynamics and the neutrino emission, which is important in order to model the neutrino signals from more complicated scenarios, such as binary neutron-star mergers. When considering nonrotating hot neutron stars we confirm earlier results of one-dimensional simulations, but also present novel results about the equilibrium properties and on how the cooling affects the stability of these configurations. In our idealized but controlled setup, we can then show that deviations from the thermal and weak-interaction equilibrium affect the stability of these models to radial perturbations, leading models that are stable in the absence of radiative losses, to a gravitational collapse to a black hole when neutrinos are instead radiated.