A Numerical Scheme for General Relativistic Radiation Magnetohydrodynamics Based on Solving a Grid-based Boltzmann Equation

We develop a general relativistic radiation magnetohydrodynamics (GR-RMHD) codeinazumain which the time-dependent radiation transfer equation (frequency-integrated Boltzmann equation) is solved in curved spacetime. The Eddington tensor is derived from the specific intensity, and we solve the zeroth and first moment equations in order to update the radiation fields. Therefore, our code can solve the radiation field around relativistic compact objects more appropriately than an approximation method like the M1 closure scheme. The numerical scheme of magnetohydrodynamics is the same as that of our previous code. In some test calculations for propagating radiation and radiation hydrodynamics in flat spacetime, our code shows similar results to our previous work. Radiation propagation in curved spacetime is also properly solved for. We also show the radiation transport from the super-Eddington accretion disk around the black hole. The disk structure, such as the density, velocity, and temperature, is fixed by the model obtained using the GR-RMHD simulation with the M1 method. We found that the difference between our scheme and the M1 method appears in the optically thin outflow region around the rotation axis while the radiation field is almost the same in the optically thick disk region.