Computer simulation of time-dependent spherically symmetric spacetimes containing radiating fluids: Formalism and code tests

Description/Abstract

We present the general equations for general-relativistic radiation hydrodynamics. We derive the 3 + 1 Einstein equations including a radiation component in the energy-momentum tensor and later specialize these equations to spherically symmetric spacetimes and the isotropic gauge. We derive the 3 + 1 equations for general relativistic hydrodynamics, including the radiation 4-force density, and we derive the 3 + 1 general relativistic Boltzmann equation, all for spherically symmetric spacetimes. These equations are then specialized to the isotropic gauge. We describe the implicit finite differencing of the Boltzmann equation and of the radiation contribution to the hydrodynamics equations. We present a new implicit numerical scheme for the matter-radiation coupling, that is, for the collision term in the Boltzmann equation and the radiation 4-force density in the hydrodynamics equations. This scheme allows for analytic matrix inversion of the finite difference equations for these terms and does not rely on partial temperatures. We describe Evans' hydrodynamics code for spherically symmetric spacetimes, which is used in conjunction with our radiation code. We then describe and present the results of a code test for the radiation transport and matter-radiation coupling that serves as a benchmark for our code. Finally, we describe and present the results of a general relativistic example and code test we have developed.