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 6D 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 1D grid in space under spherical symmetry but also a 2D spatial mesh under axisymmetry in order to assess the capability of the code to compute the spatial advection of neutrinos. Second, 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.
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