Relativistic radiation magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core-collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics (MHD), we have developed a general relativistic code capable of evolving MHD fluids and radiation in dynamical spacetimes. Our code solves the coupled Einstein-Maxwell-MHD-radiation system of equations both in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN (Baumgarte-Shapiro-Shibata-Nakamura) equations, and use a conservative, high-resolution shock-capturing scheme to evolve both the MHD and radiation moment equations. In this paper, we implement our scheme for optically thick gases and gray-body opacities. Our code gives accurate results in a suite of tests involving radiating shocks and nonlinear waves propagating in Minkowski spacetime. In addition, to test our code's ability to evolve the relativistic radiation-MHD equations in strong-field dynamical spacetimes, we study "thermal Oppenheimer-Snyder collapse" to a black hole and find good agreement between analytic and numerical solutions.