Multidimensional Boltzmann Neutrino Transport Code in Full General Relativity for Core-collapse Simulations

TL;DR

This paper introduces a new multidimensional Boltzmann neutrino transport code in full general relativity, enabling more accurate core-collapse supernova simulations by directly solving the six-dimensional phase space equations.

Contribution

The authors develop and demonstrate a novel neutrino transport code that extends previous special relativistic models to include full general relativistic effects in multidimensional simulations.

Findings

Successfully computed neutrino free streaming in Schwarzschild and Kerr spacetimes.

Validated the code's spatial advection capabilities in 1D and 2D geometries.

Produced steady neutrino distributions consistent with existing spherically symmetric models.

Abstract

We develop a neutrino transfer code for core-collapse simulations, that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the six dimensional phase space. The code is an extension of our special relativistic code coupled to a Newtonian hydrodynamics code, which is currently employed for core-collapse supernova simulations. In order to demonstrate our code's capability to treat general relativistic effects, we conduct some tests: we first compute the free streaming of neutrinos in the Schwarzschild and Kerr spacetimes and compare the results with the geodesic curves; in the Schwarzschild case we deploy not only a 1-dimensional grid in space under spherical symmetry but also a 2-dimensional spatial mesh under axisymmetry in order to assess the capability of the code to compute the spatial advection of neutrinos; secondly, we calculate the neutrino transport in a fixed matter background, which is taken from a core-collapse supernova simulation with our general relativistic but spherically symmetric Boltzmann-hydrodynamics code, to obtain a steady neutrino distribution; the results are compared with those given by the latter code.